△ABC is similar to △PQR, QR = 8 cm, BC = 4 cm and perimeter of △PQR = 32 cm. Find the perimeter of △ABC.

Correct option is C

Given:

△ABC is similar to △PQR.

QR = 8 cm, BC = 4 cm, and the perimeter of △PQR = 32 cm.

Formula Used:

In similar triangles, the ratio of corresponding sides is the same:

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

The ratio of the perimeters of two similar triangles is equal to the ratio of any pair of corresponding sides.

Solution:

The corresponding sides of the triangles △ABC and △PQR are BC and QR.

​$$(\frac{BC }{ QR}) = (\frac{4 }{ 8}) = \frac{1 }{ 2}$$​​

The ratio of the perimeters of △ABC and △PQR is the same as the ratio of corresponding sides:

(Perimeter of △ABC / Perimeter of △PQR) = 1 / 2

The perimeter of △PQR is 32 cm, so:

Perimeter of △ABC = ($$\frac{1 }{ 2}$$​) × 32 = 16 cm