Question

Find the dimensions of the cuboid which are in the ratio5:3:1 and its total surface area is 414 m sq..

Answer 1

Let the dimensions be 5x, 3x and x m.

Total Surface area of cuboid = 2(lb+bh+lh)

414=2(5x*3x+3x*x+5x*x)

207=23x^2

9=x^2

x=3

Dimensions= 5*3=15m, 3*3=9m, 3m

Answer 2

the dimentions of a cuboid is length, breadth and height
length:brradth:height=5:3:1
taking common multiple as x
therefore length=5x breadth=3x height=×
Total surface area of cuboid=
2(l×b+b×h+l×h)
=2(5x×3x+3x×x+5x×x)
=2(15x2 +3x2 +5x2)
=2(23x2)
=46x2
:. 414=46x2
x2 = 9
x. =3. (TAKING SQUARE ROOTS)
:. length. =5x=5×3=15m
breadth=3x=3×3=9m
height. =x=3m

ANSWER
dimensuons of the cubiod is 15m×9m×3m