The length of a rectangular field is 23 m more than its breadth.
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) 2420 m2
(b) 2520 m2
(c) 2480 m2
(d) 2620 m2

 

Solution:

(b) 2520 m2

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

Now,

Perimeter $=2($ Length $+$ Breadth $)=2(x+x+23)=(4 x+46) \mathrm{m}$

Thus, we have:

$4 x+46=206$

$\Rightarrow 4 x=206-46=160$

$\Rightarrow x=\frac{160}{4}=40$

∴ Breadth = x = 40 m

Length $=x+23=40+23=63 \mathrm{~m}$

Area $=$ Length $\times$ Breadth $=63 \times 40=2520 \mathrm{~m}^{2}$

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