## 9. The lengths of the sides of a triangle are in the ratio 3:4: 5and its perimeter 144 cm. find the area of the triangle

Question

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## Answers ( )

Answer:Step-by-step explanation:The ratio of the three sides is 3:4:5 and the total perimeter is 144 cm.

Three sides are say 3x +4x + 5x and they add up to 144 cm, or 12 x = 144, so x = 12. Therefore the lengths of the three sides are 36 cm, 48 cm and 60 cm.

Method 1:

Since the ratio is 3:4:5 it is a right angled triangle and the area = 36*48/2 = 12*3*12*4/2 = 144*6 = 864 sq cm. Here 60 cm is the hypotenuse

Method 2:

Area = [s(s-a)(s-b)(s-c)]^0.5 where s = perimeter/2, and a, b, and c are the three sides.

Therefore area = [72(72–36)(72–48)(72–60)]^0.5

= [ 72*36*24*12]^0.5 = [72*36*2*12*12]^0.5 = 72 * 12 = 864 sq cm. No calculator needed for this exercise!

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