Question
The perimeter of a rectangle of length 2(x + 4) cm and
breadth 2(x + 3) cm is double the perimeter of a square of area 484 cm². Find the area of the rectangle.Solution
Area of square = 484 cm² Side of square = √484 = 22 cm Perimeter of square = 22 × 4 = 88 cm So, perimeter of rectangle = 2 × 88 = 176 cm ⇒ 2(2(x + 4) + 2(x + 3)) = 176 ⇒ 4x + 14 = 88 ⇒ 4x = 74 ⇒ x = 18.5 So, length of rectangle = 2(18.5 + 4) = 45 cm And, breadth of rectangle = 2(18.5 + 3) = 43 cm Therefore, area of rectangle = 45 × 43 = 1935 cm²
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