Question

the total surface area of a cuboid is 1332cm if length breadth and height are in the ratio 6:5:4, find its dimensions

Answer 1

Let the length be 6x, breadth be 5x and height be 4x.
TSA of cuboid=2*(lb+bh+hl)
1332=2*(6x*5x+5x*4x+4x*6x)
666=30x²+20x²+24x
666=74x²
x²=9
x=3
Therefore, Length=6(3)=18 cm.
Breadth=5(3)=15 cm.
Height=4(3)=12 cm.

Answer 2

Given:-

Total surface area of cuboid = 1332 cm²

Let the length, breadth and height be 6x, 5x and 4x.

Total surface area of cuboid = 2(lb+bh+hl)
1332 = 2(6x*5x + 5x*4x + 4x*6x)
1332 = 2(30x + 20x + 24x)
1332 = 2(74x)
1332 = 148x³
x³ = 1332/148
x³ = 9
x = 3

Dimensions of cuboid :-

Length = 6x = 6*3 = 18 cm
Breadth = 5x = 5*3 = 15 cm
Height = 4x = 4*3 = 12 cm

Ans.) The dimensions of cuboid are 18 cm, 15 cm and 12 cm.