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Quizzes > High School Quizzes > Mathematics

Scale Factor Practice Test

Sharpen skills with engaging scale factor challenges

Difficulty: Moderate
Grade: Grade 8
Study OutcomesCheat Sheet
Paper art promoting Scale Factor Frenzy, a dynamic high school geometry practice quiz.

What is a scale factor in geometry?
The difference between two corresponding angles
The sum of the interior angles of a polygon
The ratio of the lengths of corresponding sides in similar figures
The ratio of the area of two similar figures
A scale factor is defined as the ratio of two corresponding linear measurements in similar figures. It is used to enlarge or reduce figures while keeping their shape proportional.
When a shape is enlarged by a scale factor k, by what factor is its area multiplied?
2k
2/k
k
k^2
The area of a scaled figure increases by the square of the scale factor because area involves two dimensions. For a scale factor of k, the area becomes k^2 times the original.
How does the perimeter of a geometric figure change when it is scaled by a factor k?
It is multiplied by k^2
It remains the same
It is divided by k
It is multiplied by k
Perimeter is a linear measurement, so when a figure is scaled by a factor k, every linear dimension including the perimeter is multiplied by k. This maintains the proportionality of the shape.
If triangle ABC is similar to triangle DEF with a scale factor of 2, what does this imply about their side lengths?
Their angles are scaled by a factor of 2
Each side of triangle DEF is twice as long as the corresponding side of triangle ABC
Triangle DEF has four times the area of triangle ABC
Each side of triangle ABC is twice as long as the corresponding side of triangle DEF
A scale factor of 2 indicates that every side in the larger triangle is twice the length of its corresponding side in the smaller triangle. The angles remain congruent, which is characteristic of similar figures.
What effect does a scale factor less than 1 have on a geometric figure?
It reduces the size of the figure
It doubles the area of the figure
It changes the shape of the figure
It enlarges the figure
A scale factor less than 1 shrinks the figure proportionally, reducing all dimensions while maintaining the same shape and proportions. This is a common transformation in similarity.
Two similar rectangles have a scale factor of 3 from the smaller to the larger. If the smaller rectangle has a perimeter of 20 units, what is the perimeter of the larger rectangle?
80
40
20
60
The perimeter of a shape scales linearly with the scale factor. Multiplying the smaller perimeter (20 units) by 3 gives the larger perimeter of 60 units.
The corresponding side lengths of two similar triangles are in the ratio 5:7. If the area of the smaller triangle is 50 square units, what is the area of the larger triangle?
90
100
70
98
The area ratio of similar triangles is the square of the linear scale factor. Since the side ratio is 5:7, the area scales by (7/5)^2 = 49/25; multiplying 50 by 49/25 yields 98 square units.
If two circles are similar with a scale factor of 4 for their radii, by what factor does their circumference increase?
4
8
16
2
Circumference is a linear measurement that directly depends on the radius. When the radius is multiplied by 4, the circumference also increases by a factor of 4.
A triangle with side lengths 3, 4, and 5 is enlarged by a scale factor of 3. What will be the new side lengths of the triangle?
6, 8, 10
3, 4, 5
12, 16, 20
9, 12, 15
Each side of the triangle is multiplied by the scale factor of 3, resulting in new side lengths of 9, 12, and 15. This transformation preserves the triangle's proportions.
If the sides of a figure are scaled by a factor of 1/2, what is the factor by which the area is scaled?
2
1
1/4
1/2
Area scales by the square of the linear scale factor. Thus, if the sides are halved (1/2), the area becomes (1/2)^2 = 1/4 of the original.
If a cube with an edge length of 2 units is scaled by a factor of 3, what is the volume of the new cube?
216
54
72
18
When a three-dimensional figure is scaled, its volume is multiplied by the cube of the scale factor. The new edge length is 2Ã - 3 = 6, and 6^3 equals 216.
In similar figures, aside from their size, which property remains unchanged?
Their side lengths
Their perimeters
Their areas
Their angles
Similar figures have congruent corresponding angles, ensuring that while their sizes may differ, their overall shape remains the same. This is a fundamental property of similarity.
If the scale factor between two similar quadrilaterals is 0.8, what is the corresponding side length in the second quadrilateral if one side of the first quadrilateral is 10 units?
0.8
8
10
12
Multiplying the given side length by the scale factor yields the corresponding side length. Here, 10 Ã - 0.8 equals 8 units.
A pair of similar pentagons have areas in the ratio 9:16. What is the scale factor for their sides from the smaller to the larger pentagon?
3/4
4/3
16/9
9/16
The linear scale factor is the square root of the area ratio in similar figures. Since √(9/16) equals 3/4, the side lengths scale by a factor of 3/4 from the smaller to the larger pentagon.
On a map drawn with a scale of 1:50000, if a road measures 2 cm on the map, what is its real-life length?
1 km
50 km
2 km
0.5 km
A scale of 1:50000 means that 1 cm on the map corresponds to 50000 cm in reality. Therefore, 2 cm corresponds to 100000 cm, which converts to 1 km.
Two similar triangles have side lengths in the ratio 7:9. If the perimeter of the smaller triangle is 42 units, what is the perimeter of the larger triangle?
63
54
56
48
The scale factor from the smaller to the larger triangle is 9/7. Multiplying the smaller triangle's perimeter of 42 units by 9/7 gives 54 units for the larger triangle.
A rectangle with dimensions 8 cm by 12 cm is enlarged to a similar rectangle with an area of 480 cm². What is the scale factor from the original rectangle to the new rectangle?
√5
√2
2
5
The original area of the rectangle is 8 à - 12 = 96 cm². Since the new area is 480 cm², the area has been multiplied by 5. Taking the square root gives a linear scale factor of √5.
For two similar polygons with a side length ratio of 3:5, if a side of the smaller polygon measures 15 units, what is the corresponding side length in the larger polygon?
20
30
25
18
Multiply the side length of the smaller polygon by the scale factor (5/3) to find the corresponding side in the larger polygon. Here, 15 Ã - (5/3) equals 25 units.
If a scale drawing is reduced using a scale factor of 1/10, by what factor is the drawing's area reduced?
1/100
10
1/20
1/10
The area of a figure is proportional to the square of the scale factor. With a scale factor of 1/10, the area is reduced by (1/10)², which is 1/100 of the original.
A model car is built with a scale factor of 1:18 relative to the actual car. If the model is 25 inches long, what is the length of the actual car?
18 inches
450 inches
125 inches
225 inches
A scale of 1:18 means every inch on the model represents 18 inches on the actual car. Multiplying the model length of 25 inches by 18 results in 450 inches.
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Study Outcomes

  1. Analyze and compute scale factors to determine dimensions of similar figures.
  2. Apply proportional reasoning to solve for missing lengths in geometric problems.
  3. Evaluate scale drawings by interpreting scale factors accurately.
  4. Demonstrate the ability to use ratios to establish relationships between parts of similar figures.
  5. Verify results by cross-checking calculated dimensions with provided scale factors.

Scale Factor Questions Cheat Sheet

  1. Scale Factor Essentials - A scale factor is your VIP pass to resizing shapes while exactly preserving their proportions! When the number is above 1, you're in enlargement territory; between 0 and 1, you're shrinking to mini size - all without warping the original. Cuemath: Scale Factor Basics
    2. Visit Cuemath for a deep dive!
  2. Finding Your Magic Number - To pinpoint the scale factor, just divide a side length in the new figure by its matching original side. If a 5‑unit side blossoms into 10 units, you land on a scale factor of 2 - math magic at work! Cuemath: Scale Factor Explained
    3. Check Cuemath for examples!
  3. Dilations Beyond the Origin - Here's a fun twist: dilations don't have to pivot at (0,0). Shift your centre point first, then apply the scale factor to see your figure dance to a new spot! SchoolTube: Dilations in Geometry
    4. Watch it in action on SchoolTube!
  4. Area Changes by the Square - When you crank up the scale factor by 3, you don't just triple the area - you square it and get 9 times more surface to color in. Always remember: area scales with the factor squared! Illustrative Math: Area Practice
    5. Try the practice problems!
  5. Perimeter Goes Linear - Up the scale factor and the perimeter follows suit in a straight line - double your scale factor, double your boundary length! It's a one‑to‑one relationship that's easy to track. Illustrative Math: Perimeter Practice
    6. Get practicing here!
  6. Circle Radius Rule - For circles, the scale factor is the new radius divided by the old radius - simple as pi. If a radius jumps from 1 to 2 units, your factor is a neat 2! ByteLearn: Circle Scale Factors
    7. Dive into the details at ByteLearn!
  7. Similar Triangles - In similar triangles, angles match perfectly and sides scale in proportion - the scale factor is your proportionality detective! Use it to unveil unknown side lengths or compare shapes. ByteLearn: Similar Triangles
    8. Explore triangle secrets!
  8. Proportional Problem Solving - Tackling scale factor questions is all about setting up side-to-side proportions, cross‑multiplying, and solving for the mystery value. It's algebra meets geometry in the most satisfying way! Oak National: Scale Factor Lessons
    9. Tune in at The National Academy!
  9. Practice Makes Perfect - Solidify your skills with hands‑on problems: dilate a rectangle of area 12 by a factor of 2 and watch it leap to 48 units² in one simple calculation. Practice really does make math dreams work! Illustrative Math: Area Practice
    10. More practice right here!
  10. Positive & Non-Zero Rule - A scale factor of zero would flatten everything into a single point - no thanks! Always pick a positive number to keep your shapes recognizable and mathematically sound. Cuemath: Scale Factor Tips
    11. Refine your understanding at Cuemath!
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