Similar Triangles: Finding Side Length When Area Ratio is 1:16 and Larger Side is 42cm

If the ratio of the areas of similar triangles is 1:16, and the length of the side of the larger triangle is 42 cm, what is the length of the corresponding side in the smaller triangle?

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Step-by-step video solution

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00:00 Find the length of the appropriate side in the small triangle
00:03 Let's mark the side with X
00:06 Find the similarity ratio
00:10 The similarity ratio equals the square root of the area ratio
00:14 Make sure to take the square root of both numerator and denominator
00:25 Isolate X
00:36 And this is the solution to the question

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1

Understand the problem

If the ratio of the areas of similar triangles is 1:16, and the length of the side of the larger triangle is 42 cm, what is the length of the corresponding side in the smaller triangle?

2

Step-by-step solution

The ratio of similarity is 1:4

The length of the corresponding side in the small triangle is:

424=6 \frac{42}{4}=6

3

Final Answer

10.5

Practice Quiz

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

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