Question

If ΔABC ∼ ΔPQR, area of ΔABC/area of ΔPQR = 900/1225 and value of side PR = 7 cm, find the value of side AC. 
1. 10 cm
2. 5 cm
3. 6 cm
4. 30 cm

Answer 1

Correct Answer - Option 3 : 6 cm

Given:

ΔABC ∼ ΔPQR

Area of ΔABC/Area of ΔPQR = 900/1225

Value of side PR = 7 cm.

Concepts used:

If ΔABC ∼ ΔPQR,

Area of ΔABC/Area of ΔPQR = (AC/PR)² =  (AB/PQ)2 = (BC/QR)² 

Calculation:

As ΔABC ∼ ΔPQR,

⇒ Area of ΔABC/Area of ΔPQR = (AC/PR)2 =  (AB/PQ)2 = (BC/QR)2

⇒ 900/1225 = (AC/PR)² 

⇒ √900/√1225 = AC/PR

⇒ 30/35 = AC/7 cm

⇒ AC = (30 × 7)/35 cm

⇒ AC = 210/35 cm

⇒ AC = 6 cm.

∴ The value of side AC is 6 cm.