Question

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

Answer 1

let the common ratio be. x
t. s. a of cuboid =2(bh+hl+lb)
1260=2(4x*2x+2x*5x +5x*4x)
1260=2(8x+10x+20x)
1260=2(38x)
1260=76x
1260/76=x
x=16.5

l=5*16.5=82.5
b=4*16.5=66
h=2*16.5=33

Answer 2

let the length = 5x
breath =4
height=2x
total surface area of cuboid=1216
2(lb+bh+hl)=1216
2(5x×4x+4x×2x+2x×5x)=1216
76x=1216
x=1216/76
x=16
length =5×16=80
breath=4×16=64
height=2×16=32