Question

the dimensions of a cubod are in the ratio 1: 2:3 and its total surface area is 88meter square find the dimensions. ​

Answer 1

Dimensions of a cuboid are in ratio 1:2:3.

Total surface area of cuboid is 88 m².

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☯ Let the dimensions of cuboid be x, 2x and 3x.

$\setlength{\unitlength}{0.68cm}\begin{picture}(12,4)\linethickness{0.3mm}\put(6,6){\line(1,0){5}}\put(6,9){\line(1,0){5}}\put(11,9){\line(0,-1){3}}\put(6,6){\line(0,1){3}}\put(4,7.3){\line(1,0){5}}\put(4,10.3){\line(1,0){5}}\put(9,10.3){\line(0,-1){3}}\put(4,7.3){\line(0,1){3}}\qbezier(6,6)(4,7.3)(4,7.3)\qbezier(6,9)(4,10.2)(4,10.3)\qbezier(11,9)(9.5,10)(9,10.3)\qbezier(11,6)(10,6.6)(9,7.3)\put(8,5.5){\sf{3x}}\put(4,6.3){\sf{2x}}\put(11.5,7.5){\sf{x}}\end{picture}$

⠀⠀

We know that,

$\star\;{\boxed{\sf{\purple{TSA_{\;(cuboid)} = 2(lb + bh + hl)}}}}$

$\quad\qquad:\implies\sf 2(x \times 2x + 2x \times 3x + 3x \times x) = 88$

$\qquad\quad\quad\quad:\implies\sf 2(2x^2 + 6x^2 + 3x^2) = 88$

$\quad\qquad\qquad\quad:\implies\sf 2(11x^2) = 88$

$\quad\qquad\quad\qquad:\implies\sf 22x^2 = 88$

$\qquad\quad\quad\qquad:\implies\sf x^2 = \dfrac{88}{22}$

$\qquad\quad\qquad\quad:\implies\sf x^2 = 4$

$\qquad\quad\quad\quad:\implies\sf \sqrt{x^2} = \sqrt{4}$

$\qquad\quad\qquad\quad:\implies{\boxed{\frak{\pink{x = 2\;m}}}}\;\bigstar$

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Therefore,

☯ Dimensions of cuboid are,

• x = 2 = 2m

• 2x = 2 × 2 = 4m

• 3x = 3 × 2 = 6m

$\therefore\;{\underline{\sf{Hence,\;the\; dimensions\;to\;cuboid\;are\;2m, 4m \; and \;6m.}}}$

Answer 2

Given:-

T.S.A = 88m²

To find:-

Dimensions of the cuboid.

Answer:-

Let the ratio be 1x, 2x and 3x.

So,

l = 1x.

b = 2x.

h = 3x.

Using,

TSA = 2 (lb + bh + hl)

=> 2 [1x(2x) + 2x(3x) + 3x(1x)] = 88

=> 2 [2x² + 6x² + 3x²] = 88

=> 2 [11x²] = 88

=> 22x² = 88

=> x² = 88/22

=> x² = 4

=> x = √4

=> x = 2m

Therefore, dimensions of the cuboid:

1x = 1 (2) = 2m

2x = 2(2) = 4m

3x = 3(2) = 6m