Similar Triangles Perimeter Problem: Calculate Using 3.5, 1.5, and 4 Units

3.51.54146

The triangles above are similar.

Calculate the perimeter of the larger triangle.

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Find the perimeter of the second triangle
00:03 The triangle's perimeter equals the sum of its sides
00:10 This is triangle 1's perimeter
00:15 Similar triangles according to given data
00:21 The ratio of triangles' perimeters equals the similarity ratio
00:26 Let's substitute appropriate values and solve for the perimeter
00:32 Let's isolate P2
00:46 Let's substitute perimeter 1's value
00:53 And this is the solution to the question

Step-by-step written solution

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1

Understand the problem

3.51.54146

The triangles above are similar.

Calculate the perimeter of the larger triangle.

2

Step-by-step solution

We calculate the perimeter of the smaller triangle (top):

3.5+1.5+4=9 3.5+1.5+4=9

Due to their similarity, the ratio between the sides of the triangles is equal to the ratio between the perimeters of the triangles.

We will identify the perimeter of the large triangle using x x :

x9=143.5 \frac{x}{9}=\frac{14}{3.5}

3.5x=14×9 3.5x=14\times9

3.5x=126 3.5x=126

x=36 x=36

3

Final Answer

36

Practice Quiz

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

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