the dimensions of the cuboid are in the ratio 2:3:4 and the total surface area is 280 m². find its dimensions
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Answers
ANSWER:-------
given the ratio between the dimensions of the cuboid 2 : 3 : 4
let the dimensions of the cuboid be 2x, 3x and 4x.
given the total surface area of the cuboid = 468cm^2
formula for the TSA of a cuboid is 2(lb + bh + lh)
⇒ 2( lb + bh + lh) = 468cm^2
⇒ (2x * 3x) + (3x * 4x) + (2x * 4x) = 468/2
⇒ 6x^2 + 12x^2 + 8x^2 = 234
⇒ 26x^2 = 234
⇒ x^2 = 234/26
⇒ x^2 = 9
⇒ x = √9
⇒ x = 3cm
hence, the dimensions of the cuboid are :-
1. 2x = 2 * 3 = 6cm
2. 3x = 3 * 3 = 9cm
3. 4x = 4 * 3 = 12cm
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