An isosceles triangle has a perimeter of 84 , | vedclass

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Question

(C) Let the equal sides be $a = 30 \, cm$ and $b = 30 \, cm$. Given the perimeter $P = 84 \, cm$,the third side $c$ is calculated as $c = P - (a + b)

Vedclass · Accepted Answer

$72 \sqrt{21} \, cm^2$

Vedclass · Answer

(C) Let the equal sides be $a = 30 \, cm$ and $b = 30 \, cm$. Given the perimeter $P = 84 \, cm$,the third side $c$ is calculated as $c = P - (a + b) = 84 - (30 + 30) = 84 - 60 = 24 \, cm$. The semi-perimeter $s = P / 2 = 84 / 2 = 42 \, cm$. Using Heron's formula,the area $A = \sqrt{s(s-a)(s-b)(s-c)}$. $A = \sqrt{42(42-30)(42-30)(42-24)}$. $A = \sqrt{42 	imes 12 	imes 12 	imes 18}$. $A = 12 \sqrt{42 	imes 18} = 12 \sqrt{756}$. Since $756 = 36 	imes 21$,we have $A = 12 	imes 6 \sqrt{21} = 72 \sqrt{21} \, cm^2$.

An isosceles triangle has a perimeter of $84 \, cm$ and each of the equal sides is $30 \, cm$. Find the area of the triangle.

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