A gardener plans to extend the length of a rectangular garden by 6 feet. Let x represent the garden's original length. The expression 7(x+6) represents the area of the garden, where 7 is the width, in feet, and (x+6) represents the extended length, in feet, of the garden. When asked for the area of the extended portion, the gardener incorrectly said it was square13 feet. Expand the expression to find the area of the extension. Then describe an error the gardener might have made. Which answer below represents the correct expansion and the correct area of the extension?

Question

A gardener plans to extend the length of a rectangular garden by 6 feet. Let x represent the​ garden's original length. The expression 7(x+6) represents the area of the​ garden, where 7 is the​ width, in​ feet, and (x+6) represents the extended​ length, in​ feet, of the garden. When asked for the area of the extended​ portion, the gardener incorrectly said it was square13 feet. Expand the expression to find the area of the extension. Then describe an error the gardener might have made. Which answer below represents the correct expansion and the correct area of the​ extension?

GPT 3.5 · Answer

To find the area of the extension, we need to expand the expression 7(x+6).

Using the distributive property, we can multiply 7 by both x and 6:

7(x+6) = 7x + 7(6) = 7x + 42

So, the correct expansion is 7x + 42.

Now, let's find the area of the extension. If the gardener incorrectly said it was square 13 feet, the area of the extension would be 13^2 = 169 square feet.

Therefore, the correct expansion is 7x + 42 and the correct area of the extension is 169 square feet.