Question

the length ,breath and height of a rectangle solid are in the ratio 5:4:2 if the total surface area 1216cm2 find the length, breath and height of the solid

Answer 1

Let the common part be x
Surface area of cuboid (rectangular solid)=2 (lb+lh+bh)
ATP
2 (5x*4x+5x*2x+4x*2x)=1216
2 (20x^2+10x^2+8x^2)=1216
2*38x^2=1216
76x^2=1216
x^2=1216/76
x^2=16
x=square root of 16
x=4
length =5x=5*4=20cm
breadth=4x=4*4=16cm
height=2x=2*4=8cm
Hope it helps:)

Answer 2

Let x be taken as common.

Ratio of length : breadth : height =

5 : 4 : 2

We know that the T.S.A = 2 ( LB + BH + LH )

Therefore,

1216 = 2 ( 5x ×4x + 4x ×2x + 2x ×5x )

$1216 = 2 \: \times \: 20 {x}^{2} + 8 {x}^{2} + 10 {x}^{2}$
$1216 = 2 \times \: 38 {x}^{2}$
$1216 = 76 {x}^{2}$
$16 = {x}^{2}$
$x = 4$
Now substituting te value of
$x$
we get,

LENGTH = 5 × 4 = 20 cm
BREADTH = 4 × 4 = 16 cm
HEIGHT = 2 × 4 = 8 cm

Hope this helps !