Question

The area of the larger rectangle is given by the expression x^2+9x+14 and the area of the smaller rectangle is given by the expression x^2+3x. Find the difference in the perimeters of the rectangles.

Answer 1

To find the difference in the perimeters of the rectangles, we need to find the perimeters first.

The area of a rectangle is equal to the length times the width. Therefore, for the larger rectangle, we can write:

x^2 + 9x + 14 = length * width

Similarly, for the smaller rectangle, we can write:

x^2 + 3x = length * width

To find the perimeter, we need to add up all four sides of the rectangle.

For the larger rectangle, the length is x+7 and the width is x+2. Therefore, the perimeter of the larger rectangle is:

P_large = 2(length + width) = 2(x+7 + x+2) = 2(2x + 9) = 4x + 18

For the smaller rectangle, the length is x+3 and the width is x. Therefore, the perimeter of the smaller rectangle is:

P_small = 2(length + width) = 2(x+3 + x) = 2(2x + 3) = 4x + 6

The difference in the perimeters of the rectangles is:

P_large - P_small = (4x + 18) - (4x + 6) = 4x - 4x + 18 - 6 = 12

Therefore, the difference in the perimeters of the rectangles is 12.