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The lengths of the sides of a triangle are in the ratio 3 : 4 : 5 and its perimeter is 144 cm. Find the area of the triangle and the height corresponding to the longest side. 

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Let the sides of a triangle are 3x, 4x and 5x. 

Now, a = 3x, b = 4x and c = 5x 

The perimeter 2s = 144 

⇒ 3x + 4x + 5x = 144 [∵ a + b + c = 2s] 

⇒ 12x = 144 

⇒ x = 12 

∴ sides of triangle are a = 3(x) = 36cm 

b = 4(x) = 48 cm 

c = 5(x) = 60 cm 

Now semi perimeter s = 1/2 (a + b + c) = 1/2(144) = 72cm

Let l be the altitude corresponding to longest side, 

∴ 1/2 × 60 × l = 864

Hence the altitude one corresponding long side = 28.8 cm

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