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Question

The difference between the semi-perimeter and the sides of a ∆ABC are 8 cm, 7 cm and 5 cm respectively. The area of the triangle is
(a) 207 cm2
(b) 1014 cm2
(c) 2014 cm2
(d) 140 cm2

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Solution

(c) 2014 cm2
Let the sides of the triangle be a cm, b cm and c cm and the semi-perimeter be s cm.
Given:
s-a=8 cm , s-b=7 cm and s-c=5 cm
By adding all these, we get:
s-a+s-b+s-c=8+7+53s-(a+b+c) =20 2s=a+b+c3s-2s=20s=20 cm

By applying Heron's formula, we get:Area of triangle = s(s-a)(s-b)(s-c)=20×8×7×5=5×4×7×5×4×2=5×4×14=2014 cm2

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