The length of the sides of a triangle are in the ratio 5 : 4 : 3 and its perimeter is 96 cm. Find height of the triangle corresponding to the longest side.
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Let "x" be the sides of the triangles
Hence the sides of triangles are 4x , 5x , 3x
As we know perimeter of triangle = a + b + c
we have 96 = 4x + 5x + 3x
96 = 12x
x = 8 cm.
Hence the sides of triangles are
4x = 32 cm
5x = 40 cm
3x = 24 cm
As the following forms a pythagorean triplet,
the side with 32 cm is perpendicular to the 24 cm side.
Hence area of triangle = 1/2 b*h = 1/2 24*32 = 384 cm^2
Hence are = 384 cm^2
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