Question

If the area of Bianca’s rectangular backyard patio is represented by the expression x2 – 18x + 81, and the length of the patio is represented by the expression x − 9:

1. what is the expression for the width of the patio? Explain and show all work.
2. what special rectangular shape is the patio? (can be determined by side lengths).
Explain and show all work.

Answer 1

1)
`width=x-9`

2) Rectangular shape is square shape patio !

Explanation:

Here we have , the area of Bianca’s rectangular backyard patio is represented by the expression x2 – 18x + 81, and the length of the patio is represented by the expression x − 9: We need to find

1. what is the expression for the width of the patio? Explain and show all work.

We know that area of rectangle =
`Length(width)`

⇒
`x^2-18x+81=(x-9)(width)`

Factorizing RHS:

⇒
`x^2-9x-9x+81=(x-9)(width)`

⇒
`x(x-9)-9(x-9)=(x-9)(width)`

⇒
`(x-9)(x-9)=(x-9)(width)`

⇒
`width=x-9`

2. what special rectangular shape is the patio?

Now , we see that

`Length = x-9\\Width=x-9`

A rectangle whose length & width are equal is known as a square ! Hence , Rectangular shape is square shape patio !