A rectangle of length 10 units and breadth 8 units is split into two squares each of area x square units and two rectangles each of area y square units. Consider the following statements :<br>1. y is <strong>ALWAYS</strong> greater than x.<br>2. y can be 15 square units.<br>Which of the above statements is/are correct?

Explanation

Total area is 10 \times 8 = 80 = 2x + 2y \implies x+y = 40. For statement 2, if y=15, then x=25. A square of area 25 has side 5. Two such 5 \times 5 squares form a 10 \times 5 rectangle, leaving a 10 \times 3 space, which can be split into two 5 \times 3 rectangles (each area 15). So y=15 is possible. Since x=25 and y=15, y is not always greater than x. Only Statement 2 is correct.

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