Q&A for How to Find Scale Factor

Enlarge the figure by multiplying each side by the scale factor.

You can find the scale factor of an irregular shape just as you would find the scale factor of a regular shape. As long as you know that the two shapes are similar, you can use one dimension on both figures to calculate the scale factor. For example, if you know the width of the shape, divide one width by the other to find the scale factor.

Yes, although the fraction could be either less than or greater than 1.

For the length, divide 3 inches into 6.5 inches, and multiply by 8 feet. For the width, divide 3 inches into 5 inches, and multiply by 8 feet.

Try 1" = 50'.

First you need to convert the millimeters to meters. There are 1,000 mm in a meter, so 4,000 mm = 4 meters. Since the scale factor is 1:20 meters, multiply the number of meters by 20 to find the similar length: 4 x 20 = 80 meters.

Multiply each dimension by 50 to get the actual length and width of the house: 20 x 50 = 1,000; 13 x 50 = 650. Then, multiply the length and width to find the area: 1,000 x 650 = 650,000 square cm.

31.75 ÷ 3.8 = 8.355, or roughly 8 1/3. The exact scale is 1 : 8.355, or about 1 : 8 1/3 (or 3 : 25). That's an unusual scale. You could call it 1 : 8, but that wouldn't be exactly accurate.

That means the scale factor is 1:4, or ¼.

3:1. (A 100% increase means a doubling in size. A 200% increase is a tripling in size.)

100.

Add the three proportional numbers together: 2 + 2 + 5 = 9. Divide 9 into 180°: 180° ÷ 9 = 20°. Multiply 20° by the largest proportional number, 5: 20° x 5 = 100°, the largest angle.

The scale is 40:48, or 5:6. (The reduction is found by dividing both 40 and 48 by 8.)

Use Method 1 above.

Unfortunately, this question cannot be answered without knowing the relationship between the shapes' areas and their volumes. Also we would have to know that the two shapes are made of exactly the same material (or we would have to know the densities of the two shapes).

If it's the volume that is reduced by a factor of 3, the new volume is 90 cubic meters. If it's the linear dimensions of the prism that are reduced by a factor of 3, you would have to know more about the shape of the prism before you could answer the question.

4:1.

It's 1:96, or 1/96 (because there are 96 inches in 8 feet).

Double each number to get rid of the fraction. The ratio will remain the same. 6 / 13½ = 12 / 27.

6 mm : 3 cm = 6 mm : 30 mm = 1:5.

The scale factor of the areas is one area divided by the other. If you divide the smaller area by the larger area, you get an ascending scale factor such as 1:2. If you divide the larger area by the smaller area, you get a descending scale factor such as 2:1.

It depends on what you're comparing. You're right: if you're comparing areas but have only the side dimensions to use, you would square a side and compare it to the original dimension to find the scale factor for the areas.

The dimensions of the larger shape are three times the respective dimensions of the smaller shape. Three squared is nine, so the area of the larger shape is nine times the area of the smaller shape. That means the smaller area is 3 cm².

(3x-5) / 32 = (5x-5) / 56. Cross-multiply: 56(3x-5) = 32(5x-5). Then 168x - 280 = 160x - 160. So 8x = 120, and x = 15. That means the sides of the first triangle are 3(15) - 5 = 40 and 5(15) - 5 = 70. So the scale factor is 32 / 40 = 56 / 70 = 4 / 5 or 4 : 5.

Find the scale factor by dividing a given dimension of one figure by the corresponding dimension of the similar figure. In this case the scale is 62 / 15.5, which reduces to 4 / 1. So the scale factor is 4:1. You could also divide the smaller dimension by the larger one, if you preferred, resulting in a scale factor of 1:4.

Let's assume the two pyramids are similar, meaning they have exactly the same shape. Their bases are rectangular, not square. The volume of a rectangular pyramid is V = 1/3 the length times the width times the height. With a scale factor of 4, the volume of the larger pyramid is (4)(4)(4) = 64 times as large as the volume of the smaller pyramid. The latter is (1/3)(3)(2)(6) = 12 cubic units. Therefore, the larger pyramid's volume is (64)(12) = 768 cubic units.

Ideally, the number line will note the scale factor in a convenient location if it's not obvious from simply inspecting the line.

If two cubes have their edges in a ratio of 5:2, their volumes will be in a ratio of 5³ : 2³ or 125 : 8. 125 ÷ 8 = 15.625. That means that the smaller cube's volume = 500 / 15.625 = 32 cubic centimeters.

In this case, you rely on the fact that there are 100,000 centimeters in a kilometer. Then 5 km equals 500,000 cm. The scale, then, is 2 : 500,000 or 1 : 250,000.

The scale of the lengths is 7:21 or 1:3. That means the scale of the areas is 1² / 3² = 1/9. So the enlarged area is 9 times larger than the original area. (9)(35) = 315 cm².