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: $A(x)=x^{2} +5x$