The perimeter of an isosceles triangle is 32 | vedclass

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(C) Let the equal sides be $3x$ and the base be $2x$.The perimeter of the triangle is the sum of all sides: $3x + 3x + 2x = 32 \, cm$.$8x = 32 \implie

Vedclass · Accepted Answer

$32 \sqrt{2} \, cm^2$

Vedclass · Answer

(C) Let the equal sides be $3x$ and the base be $2x$.The perimeter of the triangle is the sum of all sides: $3x + 3x + 2x = 32 \, cm$.$8x = 32 \implies x = 4$.Thus,the sides are $a = 12 \, cm$,$b = 12 \, cm$,and $c = 8 \, cm$.The semi-perimeter $s = \frac{32}{2} = 16 \, cm$.Using Heron's formula,Area $= \sqrt{s(s-a)(s-b)(s-c)}$.Area $= \sqrt{16(16-12)(16-12)(16-8)} = \sqrt{16 	imes 4 	imes 4 	imes 8}$.Area $= \sqrt{16 	imes 16 	imes 8} = 16 	imes 2\sqrt{2} = 32\sqrt{2} \, cm^2$.

The perimeter of an isosceles triangle is $32 \, cm$. The ratio of the equal side to its base is $3: 2$. Find the area of the triangle.

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