Question
The perimeter of a rectangle of length 2(x + 6) cm and
breadth 2(x + 5) cm is double the perimeter of a square of area 361 cm². Find the area of the rectangle.Solution
Area of square = 361 cm² Side of square = √361 = 19 cm Perimeter of square = 19 × 4 = 76 cm So, perimeter of rectangle = 2 × 76 = 152 cm ⇒ 2(2(x + 6) + 2(x + 5)) = 152 ⇒ 4x + 22 = 76 ⇒ 4x = 54 ⇒ x = 13.5 So, length of rectangle = 2(13.5 + 6) = 39 cm And, breadth of rectangle = 2(13.5 + 5) = 37 cm Therefore, area of rectangle = 39 × 37 = 1443 cm2
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