Question
The perimeter of a rectangle of length 2(x + 5) cm and
breadth 2(x + 2) cm is double the perimeter of a square of area 324 cm². Find the area of the rectangle.Solution
Area of square = 324 cm² Side of square = √324 = 18 cm Perimeter of square = 18 × 4 = 72 cm So, perimeter of rectangle = 2 × 72 = 144 cm ⇒ 2(2(x + 5) + 2(x + 2)) = 144 ⇒ 4x + 14 = 72 ⇒ 4x = 58 ⇒ x = 14.5 So, length of rectangle = 2(14.5 + 5) = 39 cm And, breadth of rectangle = 2(14.5 + 2) = 33 cm Therefore, area of rectangle = 39 × 33 = 1287 cm²
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