Question

triangle PQR is similar to triangle ABC, PQ = 6 cm, AB = 8 cm & Perimeter of triangle ABC is 36 cm , then perimeter of triangle PQR ​

Answer 1

Step-by-step explanation:

Let perimeter of PQR = x cm

According to similar triangle

PQ/ AB = Perimeter of PQR/Perimeter of ABC

$\frac{6}{8} = \frac{x}{36} \\ x = \frac{6 \times 36}{8} = 27cm$

so perimeter of PQR = 27 cm Ans.

Answer 2

Given: triangle PQR is similar to triangle ABC, PQ = 6 cm, AB = 8 cm & Perimeter of triangle ABC is 36 cm.

To find: perimeter of triangle PQR.

Solution:

When two triangles are similar, the corresponding angles between the two triangles are equal and their corresponding sides are in proportion. The corresponding sides in proportion can be written as follows.

$\frac{AB}{PQ} = \frac{BC}{QR} = \frac{AC}{PR}$

The perimeters of the two triangles are also in proportion with the sides. This proportion can be written as follows.

$(\frac{AB}{PQ} )^{2} = \frac{(P_{ABC})}{(P_{PQR})}$

$(\frac{8}{6} )^{2} = \frac{36}{(P_{PQR})}$

On rearranging, the perimeter of the triangle PQR can be found.

$P_{PQR} = \frac{36*36}{64}$

          $= 20.25 cm^{2}$

Therefore, the perimeter of triangle PQR is 20.25 cm².