Question

The length of a rectangular field is 23 m more than its breadth. If the perimeter of the field is 206 m, then its area is
(a) 1520 m²
(b) 2420 m²
(c) 2480 m²
(d) 2520 m²

Answer 1

(d) 2520 m²

Let the breadth of the field be x m.
∴ Length = (x + 23) m

Now,
Perimeter$=2(\mathrm{Length}+\mathrm{Breadth})=2(x+x+23)=(4x+46)\mathrm{m}$
Thus, we have:
$$\begin{gathered} 4x+46=206 \\ \Rightarrow 4x=206-46=160 \\ \Rightarrow x=\frac{160}{4}=40 \end{gathered}$$
∴ Breadth = x = 40 m
Length = x + 23 $=40+23=63\mathrm{m}$
Area$=\mathrm{Length}\times \mathrm{Breadth}=63\times 40=2520{\mathrm{m}}^2$