A rectangle has a height that is 5 inches less than the base. If the area of the rectangle is 57 inches square, what are the height and base of the rectangle?

The height and base of the rectangle are approximately 5.453 inches and 10.453 inches, respectively.

Step-by-step explanation:

From Geometry we remember that area of a rectangle (), measured in square inches, is equal to:

(Eq. 1)

Where:

- Width, measured in inches.

- Height, measured in inches.

In addition, we get the following relationship from statement:

(Eq. 2)

If we know that , then the height of the rectangle is:

From Quadratic Formula we obtain the following roots:

and

Only the first root offers a reasonable solution, as length has always positive values. Thus, the height of the rectangle is approximately 5.453 inches.

Now we calculate the width of the rectangle from (Eq. 1):

If we know that and , then the width of the rectangle is:

The height and base of the rectangle are approximately 5.453 inches and 10.453 inches, respectively.