Arectangle has an area of (x2 − 17x 72) square units. since the area of a rectangle is determined using the formula, a = lw, what could be the length and width of the rectangle? length = (x − 8) units and width = (x − 9) units length = (x 9) units and width = (x 8) units length = (x − 6) units and width = (x − 12) units length = (x 12) units and width = (x 6) units

 length = (x − 8) units and width = (x − 9) units

Explanation:

The area of the rectangle is

This is a second-order polynome of the form

(1)

with b=-17 and c=72. This type of polynome can be decomposed into the form

If we rewrite explicitely this last form, we have

(2)

If we compare (1) with (2), we notice that they are exactly the same form, with:

Since we know b=-17 and c=72, we have to find the two numbers and whose sum is -17 and whose product is 72. The two numbers must be both negative (since their product is positive and their sum is negative), so they are:

Therefore, the length and the width of the rectangle are

stops on an even number.