Question

the length breadth and height of a rectangular solid are in the ratio 5:4:2, if TSA is equal to 1216 cm sq. find the length breadth and height​

Answer 1

$\huge\mathbb{SOLUTION:-}$

$\sf\underline{\blue{\:\:\:\:Given:-\:\:\:\:\:}}$

● 5:4:2

● T.S.A=1216.sq.cm

$\sf\underline{\pink{\:\:\:\: Solution:-\:\:\:\:\:}}$

$\boxed{\sf{T.S.A\:of\:cuboid=2(lb+bh+lh)}}$

• Let the side be x

• 5x ,4x and 2x

Now the T.S.A

$\sf\implies 1216=2(5x\times 4x+4x\times 2x+2x\times 5x)\\ \\ \sf\implies 1216=2( 20x{}^{2}+8x{}^{2}+10x{}^{2})\\ \\ \sf\implies 1216=2\times38x{}^{2}\\ \\ \sf\implies 1216=76x{}^{2}\\ \\ \sf\implies \cancel{\dfrac{1216}{76}}=x{}^{2}\\ \\ \sf\implies 16=x{}^{2}\\ \\ \sf\implies x=\sqrt{16}\\ \\ \sf\implies x=4$

• The value of x is 4 cm

• Now the dimensions of solid

Side of soLid :-

●Length. => 5*4= 20cm

●Breadth => 4*4=16cm

●Height => 2*4=8cm

$\underline{\boxed{\mathfrak{\purple{Sides =20cm\:16cm\:and\:8cm}}}}$

Answer 2

AnSwEr :

• Length, breadth and height are in ratio of 5:4:2
• Total Surface Area = 1216 cm²

Let the length be 5x

Breadth be 4x

Height be 2x

$\rule{150}{0.5}$

We have Formula for T.S.A of Cuboid

$\large \star {\boxed{\sf{T.S.A \: = \: 2(lb \: + \: bh \: + \: hl)}}} \\ \\ \\ \small : \implies {\tt{1216 \: = \: 2 \big[ (5x \: \times \: 4x) \: + \: (4x \: \times \: 2x) \: + \: (5x \: \times \: 2x) \big] }} \\ \\ \\ : \implies {\tt{1216 \: = \: 2(20x^2 \: + \: 8x^2 \: + \: 10x^2)}} \\ \\ \\ :\implies {\tt{1216 \: = \: 2(38x^2)}} \\ \\ \\ : \implies {\tt{1216 \: = \: 76x^2}} \\ \\ \\ \implies {\tt{x^2 \: = \: \dfrac{\cancel{1216}}{\cancel{76}}}} \\ \\ \\ : \implies {\tt{x^2 \: = \: 16}} \\ \\ \\ : \implies {\tt{x \: = \: \sqrt{16}}} \\ \\ \\ : \implies {\tt{x \: = \: 4 \: cm}} \\ \\ \\ {\underline{\boxed{\sf{\therefore \: x \: = \: 4 \: cm}}}}$

$\rule{200}{2}$

Dimensions are :

$\star {\boxed{\sf{Length \: = \: 5x \: = \: 5(4) \: = \: 20 \: cm}}} \\ \\ \star {\boxed{\sf{Breadth \: = \: 4x \: = \: 4(4) \: = \: 16 \: cm}}} \\ \\ \star {\boxed{\sf{Height \: = \: 2x \: = \: 2(4) \: = \: 8\:cm}}}$