Question

the length breadth and height of a rectangular solid are in ratio of 6:5:4 if total surface area is 5328sqcm find its dimension

Answer 1

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Answer 2

The dimensions of cube are 50.88 cm , 42.4 cm and 33.92 cm

Step-by-step explanation:

We are given that The length breadth and height of a rectangular solid are in ratio of 6:5:4

Let the ratio be x

So, Length = 6x

Breadth = 5x

Height = 4x

Total surface area of solid = $2(lb+bh+hl)=2(6x \times 5x + 5x \times 4x + 4x \times x)$

We are given Total surface area is 5328 sq cm

So, $2(6x \times 5x + 5x \times 4x + 4x \times 6x) =5328$

$(30x^2 + 20x^2 + 24x^2) =5328$

$74x^2=5328x=\sqrt{\frac{5328}{74}}x=8.48$

Length = 6x=6(8.48)=50.88 cm

Breadth = 5x=5(8.48)=42.4 cm

Height = 4x=4(8.48)=33.92 cm

Hence The dimensions of cube are 50.88 cm , 42.4 cm and 33.92 cm

#Learn more:

The length, breadth, height of a rectangular solid are in ratio of 5:4:2. If total surface area 1216cm².find the length, breadth, height of the rectangular solid.

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