Discussion
A rectangle becomes a square when its length and breadth are reduced by 10 m and 5 m, respectively. During this process, the rectangle loses 650 m2 of area. What is the area of the original rectangle in square meters?
Answer: B
The original area is 2250 m2.
Let the length be l and the breadth b. The reduced sides are equal, so l - 10 = b - 5, that is, l = b + 5. The lost area is 650:
\[ \begin{aligned} lb - (l - 10)(b - 5) &= 650 \\ 5l + 10b - 50 &= 650 \\ 5(b + 5) + 10b &= 700 \\ b = 45,\ l &= 50 \end{aligned} \]
So the rectangle is 50 m by 45 m, area 2250 m2, and the square left is 40 m by 40 m (1600 m2, which is 650 less). 1125 and 4500 are half and double the answer, and 2924 does not fit the conditions.
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