Question

The Smith Family is designing new plans for an in ground pool. Mr. Smith draws a rectangular shape with a length that is 5 feet longer than the height.

A.) Write a polynomial expression in simplified form, that represents the area of the pool. Show and explain how you found the area of the pool.

Answer 1

To solve this problem you must apply the proccedure shown below:

1- The formula for calculate the area of this rectangle is:

`A=LH`

Where
`L` is the length and
`H` is the heigth.

2. Let's call identify the heigth with the variable
`x`.

3. If the length is
`5ft` longer than the heigth, you have:

`L=x+5`

4. Therefore, you can write the following polynomial expression:

`A(x)=x(x+5)\\ A(x)=x^(2) +5x`

5. If you know the value of the heigth, you can susbstitute it into the polynomial expression shown above and you will obtain the area.

Therefore, the answer is:
`A(x)=x^(2) +5x`