Question

the length ,breadth,height of a rectangular solids are in the ratio 5:4:2 if its total surface ares is 1216cm sq find the volume of the solids

Answer 1

Let the l,b and h be 5x,4x and 2x respectively.
Therefore,
TSA of rectangle=1216
2wl+2lh+2hw=1216
2(4x)(5x)+2(5x)(2x)+2(2x)(4x)=1216
76x^2=1216
5xx^2=1216/76
x^2=16
x=4

Now,putting the values of x in l,b and h,
l=5x=5x4=20cm
b=4x=4x4=16cm
h=2x=2x4=8cm

Now,
Volume of the rectangle=lbh
=20x16x8
=2560cm^3

Answer 2

let the ratio be X = 5x+4x+2x = 11x

TOTAL SURFACE AREA = 2(L*B+B*H+L*H)
1216 = 2(5x*4x+4x*2x+5x*2x)
1216= 2(20x square + 8x square+ 10x square)
1216= 38x square
1216 = 76x square
x square = 1216/76
x square = 16
x =✓16
x = 4

•°• 4x = 4*4= 16
5x= 5*4= 20
2x= 2*4 = 8
volume of rectangle= lbh
20*8*16= 2560cm


( here * means multiplication and / is division)