An isosceles triangle has a perimeter of 50,c | vedclass

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Question

(B) Let the equal sides be $a = 17\,cm$ and $b = 17\,cm$.The perimeter of the triangle is $P = 50\,cm$.Let the third side be $c$. Then,$a + b + c = 50

Vedclass · Accepted Answer

$120$

Vedclass · Answer

(B) Let the equal sides be $a = 17\,cm$ and $b = 17\,cm$.The perimeter of the triangle is $P = 50\,cm$.Let the third side be $c$. Then,$a + b + c = 50$.$17 + 17 + c = 50 \implies 34 + c = 50 \implies c = 16\,cm$.The semi-perimeter $s = P / 2 = 50 / 2 = 25\,cm$.Using Heron's formula,Area $= \sqrt{s(s-a)(s-b)(s-c)}$.Area $= \sqrt{25(25-17)(25-17)(25-16)}$.Area $= \sqrt{25 	imes 8 	imes 8 	imes 9}$.Area $= 5 	imes 8 	imes 3 = 120\,cm^2$.

An isosceles triangle has a perimeter of $50\,cm$ and each of the equal sides is $17\,cm$. Find the area of the triangle. (in $,cm^2$)

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