Question
The perimeter of a rectangle is 46 cm, and the length of
its diagonal is 17 cm. What is the area of the rectangle?Solution
Let length = l, breadth = b. Perimeter: 2(l + b) = 46 ⇒ l + b = 23 …(1) Diagonal: √(l² + b²) = 17 ⇒ l² + b² = 17² = 289 …(2) We know: (l + b)² = l² + b² + 2lb From (1): (l + b)² = 23² = 529 From (2): 529 = 289 + 2lb 2lb = 529 − 289 = 240 lb = 120 Area = l × b = 120 cm²
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