Find the area of the triangle with the side l | vedclass

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Question

(A) Let the sides of the triangle be $a = 51 \, cm$,$b = 52 \, cm$,and $c = 101 \, cm$.First,calculate the semi-perimeter $s$:$s = \frac{a + b + c}{2}

Vedclass · Accepted Answer

$510$

Vedclass · Answer

(A) Let the sides of the triangle be $a = 51 \, cm$,$b = 52 \, cm$,and $c = 101 \, cm$.First,calculate the semi-perimeter $s$:$s = \frac{a + b + c}{2} = \frac{51 + 52 + 101}{2} = \frac{204}{2} = 102 \, cm$.Now,apply Heron's formula for the area of a triangle:$	ext{Area} = \sqrt{s(s-a)(s-b)(s-c)}$$	ext{Area} = \sqrt{102(102-51)(102-52)(102-101)}$$	ext{Area} = \sqrt{102 	imes 51 	imes 50 	imes 1}$$	ext{Area} = \sqrt{(51 	imes 2) 	imes 51 	imes (25 	imes 2)}$$	ext{Area} = \sqrt{51^2 	imes 2^2 	imes 5^2}$$	ext{Area} = 51 	imes 2 	imes 5 = 510 \, cm^2$.

Find the area of the triangle with the side lengths $51 \, cm$,$52 \, cm$,and $101 \, cm$. (in $, cm^2$)

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