Let ∆ABC ~∆PQR and (ar(∆ABC))/(ar(∆QPR)) = 64/169 , If AB = 10cm, BC = 7cm and AC = 16cm, then PR(in cm) is equal to:

Let ∆ABC ~∆PQR and (ar(∆ABC))/(ar(∆QPR)) = 64/169 , If AB…

Let ∆ABC ~∆PQR and $\frac{ar(∆ABC)}{ar(∆QPR)}$ = $\frac{64}{169}$ , If AB = 10cm, BC = 7cm and AC = 16cm, then PR(in cm) is equal to:

Show answer & explanation

Correct answer: C

Explanation

The correct answer is option 13 i.e. 26

Solution :

Since the ∆ABC ~∆PQR

Then according to similarity of triangles,

Ratio of the area of triangles = ration of the squares of the sides of the triangles

⇒ 64/169 = AC²/QR²

⇒ AC/QR = 8/13

⇒ 16/QR = 8/13

⇒ QR = 13 × 2

⇒ QR = 26 cm