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5. Sides of a triangle are in the ratio of 12 : 17 : 25 and its perimeter is 540 cm. Find its area.
Answer :

Suppose that the sides in cm, are 12x, 17x and 25x.
Then, we know that 12x + 17x + 25x = 540 ...(Given, Perimeter of the triangle)
54x = 540
Thus, x = 10
So, the sides of the triangle are 12 × 10cm, 17 × 10cm, 25 × 10cm i.e., 120cm, 170cm and 250cm.
Now, we know that, s=a+b+c2
Therefore, s=120+170+2502=5402=270cm

Now, Area of triangle = 270(270?120)(270?170)(270?250) ...(Since, Heron's formula [area = s(s?a)(s?b)(s?c)])
= 270×150×100×20
= 27×10×3×15×10×100×20
= 10027×15×10×2cm2
= 1009×3×3×5×10×2cm2
= 1009×3×3×10×10cm2
= 100 × 10 × 9
Therefore, area of the given triangle is 9000cm2