Similar Triangles: Calculate Second Triangle Perimeter Given Areas 361cm² and 81cm²

Question

In similar triangles, the area of the triangles is 361 cm² and 81 cm². If it is known that the perimeter of the first triangle is 38, what is the perimeter of the second triangle?

Video Solution

Solution Steps

00:00 Find the perimeter of the second triangle
00:03 Similar triangles according to given data
00:09 The ratio of perimeters equals the square root of the areas ratio
00:24 We'll substitute appropriate values according to the given data and solve for the perimeter
00:38 Make sure to take the square root of both numerator and denominator
00:49 Isolate P2
00:59 And this is the solution to the question

Step-by-Step Solution

To begin with we can determine the perimeter of the second triangle by using the equation below.

P2P1=S2S1 \frac{P_2}{P_1}=\sqrt{\frac{S_2}{S_1}}

We insert the existing data

P238=81361 \frac{P_2}{38}=\sqrt{\frac{81}{361}}

P238=81361=919 \frac{P_2}{38}=\frac{\sqrt{81}}{\sqrt{361}}=\frac{9}{19}

Lastly we multiply by 38 to obtain the following answer:

P2=919×38=18 P_2=\frac{9}{19}\times38=18

Answer

18

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Related Subjects

Similarity ratio Similarity of Triangles and Polygons

Question Types

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