Question

Error Analysis  A gardener plans to extend the length of a rectangular garden by 7 feet. Let x represent the​ garden's original length. The expression 6 left parenthesis x plus 7 right parentheses represent the area of the​ garden, where 6 is the​ width, in​ feet, and left parenthesis x plus 7 right parentheses represent the extended​ length, in​ feet, of the garden. When asked for the area of the extended​ portion, the gardener incorrectly said it was 13 square feet. Expand the expression to find the area of the extension. Then describe an error the gardener might have made.

Answer 1

trans

Step-by-step explanation:

Answer 2

The gardener's expression correctly calculates the area of the entire garden after extension, not just the extension itself. The error was in misinterpreting the question and focusing solely on the extension, leading to the incorrect answer of 13 square feet.

Step-by-step explanation:

Expanding the expression: 6(x + 7) = 6x + 42. This represents the total area of the garden after extending its length by 7 feet.

Error analysis: The gardener likely assumed they needed to calculate the area added by the extension. This could be due to:

Misunderstanding the question and focusing on the 7-foot extension instead of the total area change.

Mistakenly interpreting "area of the extension" as the area of the rectangle formed only by the additional 7-foot length and the original width.

Therefore, while the expression itself is correct, the gardener misinterpreted the question and made an error in interpreting what "area of the extension" referred to.