Question

Ezra has a square brick patio. He wants to reduce the width by 6 feet and increase the length by 6 feet.Let xrepresent the length of one side of the square patio Write expressions for the length and width of the new patio. Then find the area of the new patio if the original patio measures 13 feet by 13 feet.

Answer 1

Step-by-step explanation:

Ezra has a square brick patio where x represents the length of one side of this square patio:

And hee wants to reduce the width by 6 feet, and increase the length by 6 feet.

The new width is x-6,

The new length is x+6.

`\begin{gathered} Expressions\text{ for the length and the width of the new patio:} \\ l=x+6 \\ w=x-6 \end{gathered}`

Then, we need to find the area of the new patio:

`A=lw`

We multiply the length by the width. The area is:

`lw=(x+6)(x-6)`

And finally, if the original measure of the sides is x=13 ft, the area of the new patio is:

`\begin{gathered} (x+6)(x-6) \\ \downarrow \\ (13+6)(13-6) \\ \downarrow \\ (19)(7) \\ \downarrow \\ 133 \end{gathered}`

Since it represents the area the units are square feet:

133 square feet.

These results are shown in option B.

Answer:

`lw=(x+6)(x-6);133\text{ square feet}`