A 3.3, m high room is half as long again as i | vedclass

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Question

(A) Let the breadth of the room be $b$ meters.Given that the length is half as long again as the breadth,so length $l = b + 0.5b = 1.5b = \frac{3}{2}b

Vedclass · Accepted Answer

$7.5\, m, 5\, m$

Vedclass · Answer

(A) Let the breadth of the room be $b$ meters.Given that the length is half as long again as the breadth,so length $l = b + 0.5b = 1.5b = \frac{3}{2}b$.The height $h = 3.3\, m = \frac{33}{10}\, m$.The volume of the room is $V = l 	imes b 	imes h = 123 \frac{3}{4}\, m^3 = \frac{495}{4}\, m^3$.Substituting the values: $(\frac{3}{2}b) 	imes b 	imes \frac{33}{10} = \frac{495}{4}$.$\frac{99}{20} b^2 = \frac{495}{4}$.$b^2 = \frac{495}{4} 	imes \frac{20}{99}$.$b^2 = 5 	imes 5 = 25$.$b = 5\, m$.Length $l = \frac{3}{2} 	imes 5 = 7.5\, m$.Thus,the length is $7.5\, m$ and the breadth is $5\, m$.

$A$ $3.3\, m$ high room is half as long again as it is wide and its volume is $123 \frac{3}{4}\, m^3$. Find its length and breadth.

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