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Question
The lengths of the sides of a triangle are in the ratio 4: 5 : 3 and its perimeter is 96 cm. Find its area.
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Solution
Let the sides of the triangle ABC be 4x, 5x and 3x
Let AB = 4x, AC = 5x and BC = 3x
Perimeter = 4x + 5x + 3x = 96
=> 12x = 96
⇒ x = `96/12`
∴ x = 8
∴ Sides are
BC = 3(8) = 24 cm, AB = 4(8) = 32 cm,
AC = 5(8) = 40 cm
Since (AC)2 = (AB)2 + (BC)2 [∵ (5x)2 = (3x)2 + (4x)2]
∴ By Pythagorus Theorem, ∠B = 90°
∴ Area of ΔABC = `1/2 ("BC")("AB") = 1/2 (24)(32)`
= `12 xx 32 = 384 "cm"^2`
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