Use scale factor properties (changes lengths but not angles). | Lines, angles, and triangles | SAT Math

Scaling changes lengths by the factor, area by its square, and leaves angles unchanged.

Core Idea

Scaling a figure multiplies every length by the scale factor but leaves all angles unchanged. Perimeter scales by $𝑘$ ; area scales by $𝑘 2$ .

Understanding

Rule: Scaling changes lengths, but not angles.

Perimeter scales by $𝑘$ .
Area scales by $𝑘 2$ .
Angles stay the same.

If only one dimension changes, use the formula with just that dimension scaled.

Step by Step

Identify the scale factor $𝑘$ .
Multiply each side length (or the perimeter) by $𝑘$ .
For area, multiply by $𝑘 2$ .
Angles remain unchanged.

Misconceptions

Thinking that scaling changes angle measures.
Multiplying area by $𝑘$ instead of $𝑘 2$ .
Confusing the scale factor with the actual length — the scale factor is a ratio.

Question

Worked Example

A triangle has a perimeter of 24 cm. A similar triangle has sides that are $32$ times as long. What is the perimeter of the larger triangle, in centimeters?

Select an answer to see the explanation