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​The perimeters of two similar triangles ∆ABC and ∆PQR are 36 cm and 24 cm respectively. If PQ = 10 cm, then what is the measure of AB?​
Question

The perimeters of two similar triangles ∆ABC and ∆PQR are 36 cm and 24 cm respectively. If PQ = 10 cm, then what is the measure of AB?

A.

203\frac{20}{3} cm

B.

2003\frac{200}{3} cm

C.

1063\frac{10\sqrt{\smash[b]{6}}}{3} cm​

D.

15 cm

Correct option is D

Given:

∆ABC ~ ∆PQR (Similar triangles)

Perimeter of ∆ABC = 36 cm

Perimeter of ∆PQR = 24 cm

PQ = 10 cm

Concept Used:

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

Solution:

ABPQ=Perimeter of △ABCPerimeter of △PQR=32\frac{AB}{PQ} = \frac{Perimeter of △ABC​ }{Perimeter of △PQR} = \frac{3}{2}​  

Substitute PQ = 10cm 

AB10=32\frac{AB}{10}=\frac{3}{2} 

AB = 10×32=1510 \times \frac{3}{2} = 15cm

AB = 15cm

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