Question

the whole surface area of a rectangular box is is 846 CM square find the length,breath and height if these dimensions are in the ratio 5:4:3

Answer 1

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Answer 2

Here's your answer!!

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Whole surface area of a rectangular box is 846cm^2.

The length,breadth and height are in ration 5:4:3.

Let the length,breadth and height be 5x ,4x,3x respectively.

We know that,
Total surface area= 2(lb+bh+hl)

A/q,

$846 = 2(5x \times 4x + 4x \times 3x + 3x \times 5x)$

$846 = 2(20 {x}^{2} + 12 {x}^{2} + 15 {x}^{2} )$

$= > 846 = 2(47 {x}^{2} )$

$= > 846 = 94 {x}^{2}$

$= > {x}^{2} = \frac{846}{94} \\ = > {x}^{2} = 9$

$= > {x}^{2} = \sqrt{9} \\ = > x = 3$

Therefore,

◆Length= 5x = 5×3=15cm

◆Breadth=4x =4×3=12cm

◆Height=3x =3×3=9cm

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Hope it helps you !! :)