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

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?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
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 written solution

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1

Understand the problem

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?

2

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

3

Final Answer

81:64

Practice Quiz

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If it is known that both triangles are equilateral, are they therefore similar?

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