Question

a rectangular solid is twice as long as it's breadth and it's height is three-fourth of its breadth. find its volume be 324 m3, find its dimensions.

Answer 1

$according \: to \: your \: question \: let \: the \: length \: be \: x \: then \\ \\ length = x \\ breadth = 2x \\ height = \frac{3x}{4} \\ \\ volume \: = l \times b \times h \\ 324 = x \times 2x \times \frac{3x}{2 } \\ \\ 324 = \frac{3 {x}^{3} }{2 } \\ \\ 3 {x}^{3} = 324 \times 2 \\ \\ {x}^{3} = \frac{648}{3} \\ \\ x = \sqrt[3]{216 } \\ \\ x = 6 \\ \\ \\ here \: l = 2x \times = 2 \times 6 = 12 \\ \\ breadth = x = 6 \\ \\ \\ h = \frac{3x}{4} = \frac{18}{4} = \frac{9}{2} \\ \\ \\ \\ \\ \\ \\ \\ check \: v = lbh = 12 \times 6 \times \frac{9}{2} = 324 \: so \: solution \: is \: true$
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