If a carpenter wants to make sure that the corner of a room is square and measures ft and ft along the walls, how long should he make the diagonal?

Step-by-step explanation:

Let w represent the width of the floor. Then the length of the floor is (w+4) and its area is ...

  A = LW

  525 = (w+4)(w)

  w^2 +4w -525 = 0

  (w -21)(w +25) = 0 . . . . factor the above

Solutions are ...

  w = 21, w = -25

We are interested in the positive solution: w = 21.

The floor is 21 feet wide and 25 feet long.

Alternate solution

Sometimes, when the factors aren't obvious, it works well to write an equation for the average of the dimensions. Here, we can represent that with x, and use (x-2) for the width, and (x+2) for the length. Then we have ...

  525 = (x-2)(x+2) = x^2 -4

  529 = x^2

  √529 = 23 = x

Then w=23 -2 = 21, and the length is w+4 = 25.