The bottom of a rectangular swimming pool has an area of 216 square feet. The length of the swimming pool is 6 feet longer than its width. What is the length?

Question

w(w+6)=216

 

What is the width,w?

Answer 1

Let's call "s" the side

 

Given:

One side is 6 feet longer than another

Area= side1 * side2

A=s(s+6)

A= 216

 

Notes:

s(s+6)=216

s²+6s=216

s²+6s-216=0

(s+18)(s-12)=0

 

Answer:

s=-18 

AND

s=12

 

Since we know length can only be negative in a sense that it is going in an opposite direction, the fact that one side is negative is unimportant. The only importance of each number is its absolute value.

 

The absolute values of each side are 18 and 12. 

The length is 6 feet longer than the width.

 

Check our work:

 

18-12=6

The length is 18.

The width is 12.

 

Double check

 

18*12= 216

Answer 2

w^2+6w-216=0

(w+18)(w-12)=0

 

The width has to be 12 then.  Width 12, length 18