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

00:11 Let's find the ratio of the triangle areas.
00:15 These triangles are similar. So, we use the similarity ratio from the given data.
00:21 Remember, the area ratio equals the square of the similarity ratio.
00:26 Now, let's substitute the similarity value and calculate the area ratio.
00:32 Don't forget to square both the top and bottom numbers.
00:40 And there you go! We've found the solution!

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

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Similarity ratio Similarity of Triangles and Polygons

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