The combined area of a rectangle

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