Question 54

The sides of a triangle having area 7776 sq. cm are in the ratio 3 : 4 : 5. The perimeter of the triangle is

Solution

Let the sides of the triangle be $$3x, 4x and 5x$$

$$\because$$ $$(3x)^2+(4x)^2 = 25x^2 = (5x)^2$$

=> These are the sides of a right angled triangle and since $$5x$$ is the longest side, it will be hypotenuse

Area of triangle = $$\frac{1}{2} * 3x * 4x$$ = 7776

=> $$x^2$$ = 1296

=> $$x = \sqrt{1296}$$ = 36

=> Perimeter of triangle = $$3x + 4x + 5x$$ = $$12x$$

= 12*36 = 432 cm

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