Sides of a triangle are in the ratio of 12: 17: 25 and its perimeter is 540cm. Find its area.
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Solution:-
The ratio of the sides of the triangle is given as 12 : 17 : 25
Now, let the common ratio between the sides of the triangle be “x”
∴ The sides are 12x, 17x and 25x
It is also given that the perimeter of the triangle = 540 cm
12x + 17x + 25x = 540 cm
=> 54x = 540cm
So, x = 10
Now, the sides of triangle are 120 cm, 170 cm, 250 cm.
So, the semi perimeter of the triangle (s) = 540/2 = 270 cm
Using Heron’s formula,
Area of the triangle
= √[s(s-a)(s-b)(s-c)]
= 9000 cm2
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