Question

The dimensions of a cuboid are in the ratio 5 : 3 : 1 and its total surface area is 414 $m^2$. Find the dimensions.

Answer 1

Ratio in dimensions = 5:3:1
Let length (l) = 5x
breadth (b) = 3x
and height (h) = x
$\therefore$ Surface area = $2(l\times b+b\times h+h\times l)$
= $2(5x\times 3x+3x\times x+x\times 5x)$
= $2(15x^2+3x^2+5x^2)=2\times 23x^2=46x^2$
$\therefore 46x^2=414\Rightarrow x^2=\frac{414}{46}=9$
$\therefore x=\sqrt{9}=3$
$\therefore$ Length = 5x = $5\times 3=15$ m
breadth = 3x = $3\times 3=9$ m
height = x=3 m