Discussion

The difference between the length and the breadth of a rectangle is 23 m. If its perimeter is 206 m, then its area is:

Answer: D

The perimeter gives the sum of the sides and the difference is given directly.

\[ 2(l + b) = 206 \quad\Longrightarrow\quad l + b = 103 \]

\[ l - b = 23 \]

Adding and subtracting the two:

\[ 2l = 126 \Rightarrow l = 63, \qquad 2b = 80 \Rightarrow b = 40 \]

\[ A = 63 \times 40 = 2520 \text{ m}^{2} \]

Halving the perimeter before pairing it with the difference is the step that turns two awkward numbers into a simple pair of simultaneous equations.

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