Question

the difference between the semi perimeter and the side of a triangle abc are 8cm 7cm and 5cm respectively.find the area of the triangle

Answer 1

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The difference between the semi perimeter and the side of the Δ are 8,7 and 5

Which Implies,

(s-a) =8 (i)
(s-b) =7 (ii)
(s-c)=5 (iii)

From the above 3 eqn

3s - (a+b+c) = 8+7+5

=>3s - 2s = 20

=> s = 20cm

∴ The area of Δ is

$\sqrt{s(s - a)(s - b) (s - c)} \\ \\ \implies \sqrt{20(8)(7)(5)} \\ \\ \implies \: \sqrt{20 ×8 ×7 × 5}$

= √4 × √5 × √4 ×√ 2 ×√ 7 ×√ 5

= 4×5√2 ×√7

= 20√14cm²

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