Similar Triangles: Finding Area Ratio from 3:4 Length Ratio

Here are two similar triangles. The ratio of the lengths of the sides of the triangle is 3:4, what is the ratio of the areas of the triangles?

1021.57.5

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Find the ratio of triangle areas
00:03 Let's mark the triangles as 1,2
00:07 Find the similarity ratio
00:15 The area ratio equals the similarity ratio squared
00:24 Make sure to square both numerator and denominator
00:35 And this is the solution to the problem

Step-by-step written solution

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1

Understand the problem

Here are two similar triangles. The ratio of the lengths of the sides of the triangle is 3:4, what is the ratio of the areas of the triangles?

1021.57.5

2

Step-by-step solution

Let's call the small triangle A and the large triangle B, let's write the ratio:

AB=34 \frac{A}{B}=\frac{3}{4}

Square it:

SASB=(34)2 \frac{S_A}{S_B}=(\frac{3}{4})^2

SASB=916 \frac{S_A}{S_B}=\frac{9}{16}

Therefore, the ratio is 9:16

3

Final Answer

9:16

Practice Quiz

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

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