The perimeter of an isosceles triangle is 306 | vedclass

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(B) Let the base of the isosceles triangle be $b$ and each equal side be $a$.Given that $a = \frac{5}{8} b$.The perimeter of the triangle is $2a + b =

Vedclass · Accepted Answer

$3468\, m^2$

Vedclass · Answer

(B) Let the base of the isosceles triangle be $b$ and each equal side be $a$.Given that $a = \frac{5}{8} b$.The perimeter of the triangle is $2a + b = 306\, m$.Substituting $a$ in the perimeter equation: $2(\frac{5}{8} b) + b = 306$.$\frac{5}{4} b + b = 306 \Rightarrow \frac{9}{4} b = 306$.$b = \frac{306 	imes 4}{9} = 34 	imes 4 = 136\, m$.Now,$a = \frac{5}{8} 	imes 136 = 5 	imes 17 = 85\, m$.The area of an isosceles triangle is given by $\frac{b}{4} \sqrt{4a^2 - b^2}$.Area $= \frac{136}{4} \sqrt{4(85)^2 - (136)^2}$.Area $= 34 \sqrt{4(7225) - 18496} = 34 \sqrt{28900 - 18496}$.Area $= 34 \sqrt{10404} = 34 	imes 102 = 3468\, m^2$.

The perimeter of an isosceles triangle is $306\, m$ and each of the equal sides is $\frac{5}{8}$ of the base. Find the area.

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