Similar Triangles: Finding Area Ratio from 9:8 Length Ratio

Question

The triangle ABC is similar to the triangle DEF.

The ratio between the lengths of their sides is 9:8.

What is the ratio between the areas of the triangles?

Video Solution

Solution Steps

00:00 Find the ratio of triangle areas
00:03 The triangles are similar and this is the similarity ratio according to the given data
00:07 The area ratio equals the similarity ratio squared
00:13 Let's substitute the similarity ratio value and solve for the area ratio
00:21 Make sure to square both numerator and denominator
00:29 And this is the solution to the question

Step-by-Step Solution

We multiply the ratio by 2

9:8=18:16 9:8=18:16

Raised to the power of 2:

92:82=81:64 9^2:8^2=81:64

Answer

81:64

More Questions

Related Subjects

Similarity ratio Similarity of Triangles and Polygons

Question Types

The Ratio of Similarity: Applying the formula