A gardener plans to extend the length of a rectangular garden by 7 feet. Let x represent the garden's original length. The expression 9(x+7) represents the area of the garden, where 9 is the width, in feet, and represents the (x+7) extended length, in feet, of the garden. When asked for the area of the extended portion, the gardener incorrectly said it was 16 square feet. Expand the expression to find the area of the extension.

Question

A gardener plans to extend the length of a rectangular garden by 7 feet. Let x represent the​ garden's original length. The expression 9(x+7) represents the area of the​ garden, where 9 is the​ width, in​ feet, and  represents the (x+7) extended​ length, in​ feet, of the garden. When asked for the area of the extended​ portion, the gardener incorrectly said it was 16 square feet. Expand the expression to find the area of the extension.

Bot GPT 3.5 · Answer

To expand the expression for the area of the garden, we multiply the width (9 ft) by the extended length (x+7 ft). So, the area of the garden is 9(x+7) square feet. The gardener incorrectly said the area of the extension was 16 square feet. To find the area of the extension, we subtract the area of the original garden (9x square feet) from the total area of the garden (9(x+7) square feet): Area of the extension = Total area of the garden - Area of the original garden = 9(x+7) - 9x = 9x + 63 - 9x = 63 square feet. Therefore, the area of the extension is 63 square feet.