Q21 of 99 Page 267

The difference of length of each side of a triangle from its semiperimeterare 8 cm, 7 cm and 5 cm respectively. The area of triangle is

Let the semi perimeter of the triangle be x cm


Then the length of three sides of the triangle is


x - 8, x - 7 and x - 5 cm


Semi-perimeter of the triangle =


Where a, b and c are the sides of the triangle.


⇒


⇒ 2x = 3x – 20


⇒ x= 20


Hence the semi perimeter = 20 cm


Sides of triangle are 12 cm, 13cm and 15cm


Area of triangle =


=


=


=


= 20√14 cm2


Hence the correct option is C

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