The perimeter and one of two equal sides of an isosceles triangle are 72 cm and 20 cm respectively. Area of the triangle is:

Question

Question

Answer 1

Given,

One of two equal sides of an isosceles triangle, a = 20 cm

Perimeter of the triangle = 72 cm

Formula:

Perimeter of an isosceles triangle = 2a + b

Area of an isosceles triangle = (b/4) × √(4a² – b²)

Calculation:

Let a = 20 cm

2a + b = 72

⇒ 2 × 20 + b = 72

⇒ 40 + b = 72

⇒ b = 72 – 40

⇒ b = 32

Area of isosceles triangle = (32/4) × √(4 × 20² – 32²)

⇒ 8 × √(4 × 400 – 1024)

⇒ 8 × √(1600 – 1024)

⇒ 8 × √576

⇒ 8 × 24

⇒ 192 cm²

∴ Area of the triangle is 192 cm².

Alternate solution

Third side = 72 – 2 × 20 = 72 – 40 = 32

Semi perimeter, s = 72/2 = 36

Now,

Area = √[s (s – a) (s – b) (s – c)] = √[36(36 – 32)(36 - 20)(36 - 20)] = √(36 × 4 × 16 × 16) = 16 × 4 × 3 = 192 cm²