The side of a square is \(\frac{3}{4}\) times the length of a rectangle. The breadth of the rectangle is 1 cm more than the side of the square. If the area of the rectangle is 56 cm\(^2\), find the area of the square.

49 cm²
64 cm²
36 cm²
100 cm²

Correct answer: 36 cm²

Solution

Let the side of the square be \(x\). Then the rectangle’s length is \(\frac{4}{3}x\) and breadth is \(x+1\). Using area 56 gives \(\frac{4}{3}x(x+1)=56\), which yields \(x=6\). Therefore, the square’s area is \(6^2=36\) cm\(^2\).

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