Let △ABC ~ △PQR and [Image] = 144/49 . If AB = 12 cm, BC = 7 cm and AC = 9 cm, then PR (in cm) is equal to:

Let △ABC ~ △PQR and [Image] = 144/49 . If AB = 12 cm, BC =…

Let △ABC ~ △PQR and = $\frac{144}{49}$ . If AB = 12 cm, BC = 7 cm and AC = 9 cm, then PR (in cm) is equal to:

Show answer & explanation

Correct answer: C

Explanation

The correct answer is option 3 i.e. $\frac{21}{4}$

Given :

△ABC ~ △PQR and = $\frac{144}{49}$

AB = 12 cm, BC = 7 cm and AC = 9 cm

Concept used :

Similarity of triangles

= (AB/PQ)² = (BC/QR)² = (AC/PR)² ----- (1)

Calculations :

⇒ Using equation (1), we get

⇒ $\frac{144}{49} = (\frac{AC}{PR})^2$

⇒ $\sqrt{\frac{144}{49}} = \frac{9}{PR}$

⇒ (12/7) = 9/PR

⇒ PR = (7 × 3)/4

⇒ PR = 21/4