A prism with a right triangular base is 25 cm high. If the

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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 cm³, what is the length of the longest side of the triangle?

Volume of prism = Area of base × height

⇒ 100 =	1	× x × 2x × 25
	2

⇒ x² =	100	= 4
	25

⇒ x = 2
∴ Smaller sides of triangle = 2 cm and 4 cm
∴ Largest side = √2² + 4²
= √4 + 16 = √20
= 2√5 cm.
[∵ The triangle is right angled.]