Question

SO
2:28
The perimeters of two similar triangles are 12 cm and 24 cm respectively.
If one side of first triangle is 3 cm, find the corresponding side of the
second triangle.​

Answer 1

The corresponding side of the second triangle is 6 cm.

Step-by-step explanation:

Let the two similar triangles be "∆ABC” & “∆PQR” respectively.

So,  

The perimeter of ∆ABC = 12 cm ….. (i)

The perimeter of ∆PQR = 24 cm …. (ii)

Also, one of the side of the first triangle i.e., AB of ∆ABC = 3 cm ….. (iii)

We know that the ratio of perimeters of similar triangles is equal to the ratio of their corresponding sides, i.e.,  

[Perimeter(∆ABC)] / [Peimeter(∆PQR)] = [AB] / [PQ] ….. (iv)

Thus, substituting the given values from (i), (ii) & (iii) in (iv), we get

[Perimeter(∆ABC)] / [Peimeter(∆PQR)] = [AB] / [PQ]

⇒ $\frac{12}{24}$ = $\frac{3}{PQ}$

⇒ PQ = $\frac{3 * 24}{12}$  

⇒ PQ = 6 cm