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IF THE AREAS OF THE ADJACENT FACES OF A RECTANGULAR BLOCK ARE IN THE RATIO 2:3:4 AND ITS VOLUME IS 9000 cm3,THEN find its dimension

Answer»

Let the dimensions be
length: L, BREADTH: B and height: H
Given, LBH = 9000

Given, the ratio of FACE area
LB : BH : LH = 2:3:4

Therefore, let the face areas be 2x, 3x, 4x
LB × BH × LH = 2x × 3x × 4x
(LBH)² = 24x³
9000² = 24x³
x = 150

Thus,
LB = 2×150 = 300
BH = 3×150 = 450
LH = 4×150 = 600

Therefore,
length, L = LBH/BH = 9000/450 = 20 cm
breadth, B = LBH/LH = 9000/600 = 15 cm
height, H = LBH/LB = 9000/300 = 30 cm


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