Question

The width w of a rectangular swimming pool is 7x2. The area A of the pool is 7x3 – 42x2. What is an expression for the length of the pool? Show your work.

Answer 1

A = length · width

7x3 - 42x2 = L(7x2) Factor left side
7x2(x - 6) = L(7x2) Divide both sides by 7x2
x - 6 = L

The length of the pool is x - 6.

Note: Length is always longer than width. Although the algebra is correct, it is doubtful that x - 6 is greater than 7x2.

Answer 2

Length (L) = x - 6 .

Explanation:

Given : The width w of a rectangular swimming pool is 7x². The area A of the pool is 7x³ – 42x².

To find : What is an expression for the length of the pool? Show your work.

Solution : We have given

Width = 7x².

Area of rectangle = 7x³ – 42x².

Let the length = L

Area of rectangle = length * width .

Plugging the values.

7x³ – 42x²= L * 7x².

On dividing both sides by 7x².

`(7x^(3)-42x^(2))/(7x^(2))`.

`(7x^(3) )/(7x^(2) ) -(42x^(2) )/(7x^(2))`.

x - 6 = Length.

Therefore, Length (L) = x - 6 .