Question

The length of a rectangular hall is 5 cm more than its breadth. If the area of the hall is 750 m², then its length is
(a) 15 m
(b) 22.5 m
(c) 25 m
(d) 30 m

Answer 1

Disclaimer : -The length is given in centimetres. It should be in metres.

(d) 30 m

Let the length of the rectangle be x m.
∴ Breadth of the rectangle$=(x-5)\mathrm{m}$

$$\begin{gathered} \mathrm{Area}=x(x-5)=x^2-5x \\ \Rightarrow x^2-5x=750 \end{gathered}$$
$$\begin{gathered} \Rightarrow x^2-5x-750=0 \\ \Rightarrow x^2-30x+25x-750=0 \\ \Rightarrow x(x-30)+25(x-30)=0 \\ \Rightarrow (x+25)(x-30)=0 \\ \Rightarrow x+25=0\mathrm{and}x-30=0 \\ \Rightarrow x=-25\mathrm{and}x=30 \end{gathered}$$

Length cannot be negative.
∴ Length = x = 30 m