Question

Find the area of the base of a box of height $4cm$ and lateral surface area $120c{m}^2$, if its length is twice its breadth.

Answer 1

Let $l$ and $b$ be the length and breadth of box.

Therefore,

$l=2b$

Height of box $\left(h\right)=4cm$

Lateral surface area of box $=120{cm}^2\left(\text{Given}\right)$

As we know that,

Lateral surface area of cuboid $=2h(l+b)$

$\therefore 2\times 4(2b+b)=120$

$\Rightarrow 3b=\frac{120}{8}$

$\Rightarrow b=\frac{15}{3}=5cm$

Therefore,

Length of box $=l=2b=2\times 5=10cm$

Therefore,

Area of base of box

$=l\times b=10\times 5=50{cm}^2$