Question

The dimensions of a cuboid is in the ratio 1:2:3 it's T.S.A is :85m² . Find it's dimensions andL.S.A

Answer 1

$\blue{\bold{\underline{\underline{Answer:}}}}$

$\green{\therefore{\text{Dimension\:of\:cuboid=1.96\:cm,3.92\:cm,5.88\:cm}}}$

$\green{\therefore{\text{L.S.A\:of\:cuboid=69.1488\:cm}^{2}}}$

$\orange{\bold{\underline{\underline{Step-by-step\:explanation:}}}}$

$\green{ \underline \bold{given : }} \\ : \implies \text{Length(l) = x \: cm} \\ \\ : \implies \text{Breadth(b) = 2x\: cm} \\ \\ : \implies \text{Height(h) = 3x \: cm} \\ \\ :\implies \text{T.S.A\:of\:cuboid=85 m}^{2} \\ \\ \red{ \underline \bold{to \: find : }} \\ : \implies \text{Dimensions \: of \: cuboid = ? }\\\\ :\implies \text{L.S.A\:of\:cuboid=?}$

• According to given question :

$\bold{As \: we \: know \: that} \\ : \implies \text{T.S.A \: of \: cuboid} = 2(lb + bh + hl) \\ \\ : \implies 85 = 2(x \times 2x + 2x \times 3x + 3x\times x) \\ \\ : \implies 85 = 2(2x^{2} + 6x^{2} + 3x^{2}) \\ \\ : \implies 85 = 22x^{2} \\\\ :\implies x=\sqrt{3.86} \\ \\ \green{: \implies \text{x= 1.96 \:{cm}}^{2} }$

$\bold{Dimension} \\ \green{ : \implies \text{Length = 1.96 \: cm}} \\ \\ \green{ : \implies \text{Breadth = 3.92 \: cm}} \\ \\ \green{ : \implies \text{Height = 5.88 \: cm}} \\ \\ \bold{As \: we \: know \: that} \\ : \implies \text{L.S.A \: of \: cuboid =} 2(l + b) \times h \\ \\ \implies \text{L.S.A \: of \: cuboid =}2(1.96 + 3.92) \times 5.88 \\ \\ \implies \text{L.S.A \: of \: cuboid =}2 \times 5.88 \times 5.88 \\ \\ \green{: \implies \text{L.S.A\: of \: cuboid =}69.1488 {cm}^{2} }$