Question

Size of triangle are in ratio 5:12:13 and it's perimeter is 150m .find the area of triangle ( hero's formula)

Answer 1

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Answer 2

Let the 1st side of the triangle = 5x

the 2nd side of the triangle =12x

the 3rd side of the triangle = 13x

Then ,

According to the question,

5x + 12x + 13x = 150

30x = 150

So, x= 150/30

=5

Hence, the 1st side of the triangle = 5×5=25

the 2nd side of the triangle = 12×5=60

the 3rd side of the triangle = 13×5=65

Since, the triangle is a right triangle

= {5}^{2} + {12}^{2} = {13}^{2}

25+144=169

169=169

So, the Area of the triangle = 1/2×b×h

= 1/2 ×25×(60)

= 750 m²