Hello, fladam!

A square and a rectangle have equal perimeters.

The length of the rectangle is 11cm.

The area of the square is 4cm² larger than the area of the rectangle.

Find the length of a side on the square. Code:

* - - - - *
* - - - - - * | |
| | | | x
w | 11w | | x² |
| | | |
* - - - - - * * - - - - *
11 x

The perimeter of the rectangle is:

The perimeter of the square is:

The perimeters are equal: .

The area of the rectangle is:

The area of the square is:

The area of the square is 4 more than that of the rectangle: .

Substitute [1] into [2]: .

Factor: .

And we have two solutions: .

~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~

**Check**

If , substitute into [1]: .

The rectangle is 7 × 11.

Its perimeter is 36 cm.

Its area is 77 cm².

The square is 9 × 9.

Its perimeter is 36 cm.

Its area is: 81 cm².

. . - - - - - - - - - -

If , then: .

The rectangle is: 15 × 11.

Its perrimer is 52 cm.

Its area is: 165 cm².

The square is: 13 × 13.

Its perimeter is: 52 cm.

Its area is: 169 cm².

Both solutions check out!