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

Answer:

Length (L) = x - 6 .

Step-by-step 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.

$\frac{7x^{3}-42x^{2}}{7x^{2}}$.

$\frac{7x^{3} }{7x^{2} } -\frac{42x^{2} }{7x^{2}}$.

x - 6 = Length.

Therefore, Length (L) = x - 6 .

Answer 2

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.