A prism with a right triangular base is 25, c | vedclass

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(B) The volume of a prism is given by $V = 	ext{Area of base} 	imes 	ext{height}$.Given $V = 100\, cm^3$ and height $h = 25\, cm$.Therefore, $	ext

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$2\sqrt{5}\, cm$

Vedclass · Answer

(B) The volume of a prism is given by $V = 	ext{Area of base} 	imes 	ext{height}$.Given $V = 100\, cm^3$ and height $h = 25\, cm$.Therefore, $	ext{Area of base} = \frac{V}{h} = \frac{100}{25} = 4\, cm^2$.The base is a right-angled triangle. Let the shorter sides be $x$ and $2x$.The area of the right-angled triangle is $\frac{1}{2} 	imes 	ext{base} 	imes 	ext{height} = \frac{1}{2} 	imes x 	imes 2x = x^2$.Equating the area, $x^2 = 4$, which gives $x = 2\, cm$.The sides of the triangle are $x = 2\, cm$ and $2x = 4\, cm$.The longest side (hypotenuse) is $\sqrt{x^2 + (2x)^2} = \sqrt{2^2 + 4^2} = \sqrt{4 + 16} = \sqrt{20} = 2\sqrt{5}\, cm$.

$A$ prism with a right triangular base is $25\, cm$ high. If the shorter sides of the triangle are in the ratio of $1: 2$ and the volume of the prism is $100\, cm^3$, what is the length of the longest side of the triangle?

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