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Question

(A) Let the side of the equilateral triangle base be $a$ and the height of the prism be $h$.Lateral surface area of the prism $= 3 	imes a 	imes h =

Vedclass · Accepted Answer

$4$

Vedclass · Answer

(A) Let the side of the equilateral triangle base be $a$ and the height of the prism be $h$.Lateral surface area of the prism $= 3 	imes a 	imes h = 120 \, cm^2$.$	herefore a 	imes h = \frac{120}{3} = 40 \, cm^2 \dots (1)$Volume of the prism $=$ Area of base $	imes$ height $= \frac{\sqrt{3}}{4} a^2 	imes h = 40 \sqrt{3} \, cm^3$.$\Rightarrow a^2 	imes h = \frac{40 \sqrt{3} 	imes 4}{\sqrt{3}} = 160 \, cm^3 \dots (2)$Dividing equation $(2)$ by $(1)$:$\frac{a^2 	imes h}{a 	imes h} = \frac{160}{40}$$a = 4 \, cm$.Thus,the side of the base is $4 \, cm$.

The base of a right prism is an equilateral triangle. If the lateral surface area and volume are $120 \, cm^2$ and $40 \sqrt{3} \, cm^3$,respectively,then the side of the base of the prism is ...... $cm$.

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