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Question

The difference between the semiperimeter and the sides of a ΔABC are 8 cm, 7 cm and 5 cm respectively. Find the area of the triangle.


Solution

the difference between semi perimeter (s) and sides of a triangle are 8,7, and 5 
which means 

(s-a) =8 
(s-b) = 7
(s-c) = 5 

where a,b,c are the length of the sides of the triangle ABC 
Let the semi-perimeter of the triangle be s.
Let the sides of the triangle be a, b and c.
Given:s – a = 8,s – b = 7 ands – c = 5
Adding all the above equations, we get
(s – a) + (s – b) + (s – c) = 8 + 7 + 5
⇒ 3s – (a + b + c) = 20
⇒ 3s – 2s = 20        (a+b+c2)
⇒ s = 20 cm

Area of the triangle formula 

s(sa)(sb)(sc)

=20 × 8 ×7 × 5

5600

=74.83 cm2

 

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