Correct Answer - Option 1 : 15/7 cm

**Given:**

ΔABC ~ ΔPQR

Area of ΔABC = 25 cm^{2}

Area of ΔPQR = 49 cm^{2}

Length of QR = 3 cm

**Concept used:**

The ratio of the area of any two similar triangles is equal to the ratio of the squares of their corresponding sides.

If ΔABC ~ ΔPQR,

ar(ΔABC)/ar(ΔPQR) = (AB)^{2}/(PQ)^{2} = (BC)^{2}/(QR)^{2} = (AC)^{2}/(PR)^{2}

**Calculation:**

Let the length of BC be x.

ΔABC ~ ΔPQR

ar(ΔABC)/ar(ΔPQR) = (BC)2/(QR)^{2}

⇒ (25/49) = (x^{2})/(3)^{2}

⇒ (25/49) × 9 = x^{2}

⇒ (5/7) × 3 = x

⇒ x = 15/7

**∴ The length of the side BC is 15/7.**