Question
The combined area of a rectangle
and a square is 244 cm². The breadth of the rectangle is 4 cm longer than the side of the square. If the rectangle’s length is 15 cm, find the difference between the perimeters of the rectangle and the square.Solution
Let the length of each side of the square be ‘x’ cm Therefore, breadth of the rectangle = (x + 4) Area of the rectangle = 15(x + 4) cm2 Area of the square = x2 cm2 According to the question, 15(x + 4) + x2 = 244 Or, x2 + 15x + 60 – 244 = 0 Or, x2 + 15x – 184 = 0 Or, x2 – 8x + 23x – 184 = 0 Or, x(x – 8) + 23(x – 8) = 0 Or, (x – 8)(x + 23) = 0 Or, x = 8, -23 Since, the length cannot be negative therefore, x = 8 Breadth of rectangle = x + 4 = 12 cm Perimeter of rectangle = 2(12 + 15) = 2 × 27 = 54 cm Each side of the square = x = 8 cm Perimeter of the square = 4 × 8 = 32 cm Required difference = 54 - 32 = 22 cm
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