Question

the difference between the semi perimeter and the sides of a triangle ABC are 6cm,4cm,and 2cm.find the area of a triange ABC.​

Answer 1

$\sf\large\underline\purple{Given:—}$

the difference between the semi perimeter and the sides of a triangle ABC are 8cm,6cm,and 4cm.

$\sf\large\underline\purple{To\:find:—}$

find the area of a triange ABC

$\sf\large\underline\purple{Solution:—}$

a = 8 cm,b= 6 cm and c= 4 cm, where a,b,c are the sides of the triangle

$\sf{\implies s = \dfrac{a+b+c}{2}}$

$\sf{\implies s = \dfrac{8+6+4}{2}}$

$\sf{\implies s = 9}$

Area of the triangle:-

$\sf{\implies \sqrt{s(s-a)(s-b)(s-c)}}$

$\sf{\implies \sqrt{9(9-8)(9-6)(9-4)}}$

$\sf{\implies \sqrt{9×1×3×5}}$

$\sf{\implies \sqrt{135}}$

$\sf{\implies 3√15 cm²}$

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