Question

the perimeters of a square and rectangle are equal. one side of a rectangle is 11cm and the area of the square is 4cm^2 more than the area of the rectangle. find the side of the square.

Answer 1

The side of the square can be 13 or 9

Explanation:

Let x equal the unknown side of the rectangle and y equal the side of the square. The given information is that the area of the square is 4cm^2 larger than that of the rectangle. Mathematically this can be represented as

`11x+4=y^2`

The second known is that their perimeters are equal so,

`22+2x=4y`

Solve the first equation in terms of x and substitute it into the second and you get the quadratic

`y^2-22y+117=0`

`(y-13)(y-9)=0`

Therefore your side length for the square can be either of those.