The sides of a triangle having area 7776 sq.cm are in the ratio 3:4:5. The perimeter of the triangle is ____
Question
Geometry:
The sides of a triangle having area 7776 sq.cm are in the ratio 3:4:5. The perimeter of the triangle is ____
Let the sides of a triangle = 3x, 4x and 5x respectively
Semi perimeter, S = (a+b+c)/2 = 6x
Area of triangle = √[s(s-a)(s-b)(s-c)]
= √ [6x(6x-3x)(6x-4x)(6x-5x)]
=√ [6x(3x)(2x)(1x)]
=√ (36x4) = 6x2
Then, 6x2 = 7776 => x2 = 1296 => X = 36
Now, the Perimeter = a+b+c = 12X = 12 x 36 = 432 cm.
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