Question

Please help my test is this week ;/

The perimeters of a square and a rectangle are equal. One side of the rectangle is 11 cm and the area of the square is 4 cm2
more than the area of the rectangle. Find the side of the square.


The answer is X= 9 cm or X= 13 cm

Answer 1

Explanation:

Let x=one side of the square; y=one side of the rectangle:

The perimeters are equal, so 4x=2y+22, or y=2x-11. The areas are given by x^2, and 11(2x-11). Since the square is 4 cm^2 larger than the rectangle, we get:

x^2-4=11(2x-11)

x^2-4=22x-121

x^2-22x+117=0

(x-13)(x-9)=0

x=13, or 9

Plugging 13 into our original equation, we get a square 13X13 or 169cm^2, and a rectangle (26-11)X 11, or 165cm^2, which satisfies our requirements!!!!!!