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Sides of a triangle are in the ratio 5 ∶ 5 ∶ 8 If area of the triangle is 6912 cm2, then what is the perimeter of the triangle?

Sides of a triangle are in the ratio 5 ∶ 5 ∶ 8 If area of the triangle is 6912 cm2, then what is the perimeter of the triangle? Correct Answer 432 cm

Given:

Sides of a triangle are in the ratio 5 ∶ 5 ∶ 8

Area of the triangle is 6912 cm2

Formula used:

Area of Isosceles triangle = b/4

Perimeter of Isosceles triangle = 2a + b,

a = equal side, b = other side

Calculation:

Let the sides of a triangle be 5x, 5x, and 8x.

Area of Isosceles triangle = b/4

⇒ 6912 = 8x/4√(100x2 - 64x2)

⇒ 6912 = 2x × 6x

⇒ 12x2 = 6912

⇒ x = 24 cm

Perimeter of Isosceles triangle = 5x + 5x + 8x = 18x = 18 × 24 = 432cm.

∴ The perimeter of the triangle is 432 cm.

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