Would you help me find the dimensions of this rectangle and square?

The combined area of a square and a rectangle is 32 sq in. The width of the rectangle is 2 in. more than the length of the square, and the length of the rectangle is 3 in. more than the rectangle's width. Find the dimensions of both.

Would you help me find the dimensions of this rectangle and square?
Let x equal the square's length.





x^2 + ((x+2)((x+2)+3)) = 32


x^2 + ((x+2)(x+5)) = 32


x^2 + (x^2 + 5x + 2x + 10) = 32


2x^2 + 7x + 10 = 32


2x^2 + 7x = 22


x = 2





Therefore the square is 2" by 2" and the rectangle is 4" by 7". 2 * 2 + 4 * 7 = 4 + 28 = 32 square inches.