The ratio of the length of each equal side and the third side of an isosceles triangle is 3 ∶ 5. If the area of the triangle is \(30\sqrt{11}\) cm² then the length of the third side (in cm) is:

Question

Question

This question was previously asked in

SSC CGL 2023 Tier-I Official Paper (Held On: 18 Jul 2023 Shift 2)

Answer 1

Given:

Length of each equal side of an isosceles triangle (b) = 3x

Length of an unequal side of an isosceles triangle (a) = 5x

Area of triangle = 30√11 cm²

Formula used:

Area of isosceles triangle = (a/4) × √{(4 × b²) - a²}

Calculation:

Area of isosceles triangle = (a/4) × √{(4 × b2) - a2}

⇒ 30 × √11 = (5x/4) × √{(4 × (3x)²) - (5x)²}

⇒ 30 × √11 = (5x/4) × √{(4 × 9x2) - 25x2}

⇒ 30 × √11 = (5x/4) × √{36x2 - 25x2}

⇒ 30 × √11 = (5x²/4) × √11

⇒ x2/4 = 6

⇒ x = √24 = 2√6

Length of an unequal side of an isosceles triangle (a) = 5x

⇒ 5 × 2√6 = 10√6 cm

∴ The correct answer is 10√6 cm.

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