Question

LMN is an isosceles triangle with hypotenuse √20 units. Find the area of an isoceles triangle.
1. 10 sq.units
2. 5 sq.units
3. 16 sq.units
4. 18 sq.units

Answer 1

Correct Answer - Option 2 : 5 sq.units

Given

Hypotenuse of isoceles right angled triangle = √20 units

Concept

(Hypotenuse)² = (Perpendicular)² + (Base)²

Calculation

Let the perpendicular and base is x units

(√20)² = x² + x²

⇒ 20 = 2x²

⇒ 10 = x²      ---- (1)

Area of triangle = (1/2) × base × height

⇒ (1/2) × x × x

⇒ (1/2) × x²

⇒ (1/2) × 10 (from 1)

⇒ 5 sq.units

∴ Area of triangle is 5 sq.units.