Question

If the lengths of the sides of a triangle are in the ratio 3:4:5 and its perimeter is
48 cm, find its area.

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Answer 1

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Let The Side of The Triangle Be a, b, c,

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Let The Common Ratio Be x

∴ a = 3x

∴ b = 4x

∴ c = 5x

Perimeter = a + b + c

⠀⠀⠀⠀⠀⠀48 = 3x + 4x + 5x

⠀⠀⠀⠀⠀⠀48 = 12x

⠀⠀⠀⠀⠀⠀⠀x = 48/12

⠀⠀⠀⠀⠀⠀x = 4

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Hence..,

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The sides of a triangles are..,

a = 3x ➟ 12cm

b = 4x ➟ 16cm

c = 5x ➟ 20cm

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By Using The Heron's Formula..,

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Area of the triangle is ;

s = ( a + b + c ) / 2 = 24cm

Area^2 ➟ 24( 24 - 12 ) ( 24 - 16 ) (24 - 20 )

⠀⠀⠀⠀➟ 24 × 8 × 12 × 4

⠀⠀⠀⠀➟ 4 × 4 × 6 × 6 × 2 × 2 × 2 × 2

⠀⠀⠀⠀➟ 4 × 6 × 2 × 2

⠀⠀⠀ ➟ 96

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Hence..,

The Area of The Triangle is 96cm²

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