Question

Higher Order Thinking a carpenter plans to extend the length of rectangular desk by 7 feet. Let x represent the desk's original length. The expression 96 + 7) represents the area of the desk surface where 9 is the width, in feet, and () represents the extended length, in feet, of the desk. The carpenter thinks that the area of the extended portion of the desk is 16 square feet Which choice below includes the expanded form of the area expression for the deck's surface and the correct area of the extended portion of the desk's surface?

a. 10x + 16 and 10k square feet
b. 9x+63 and 9x square feet
c. 9x + 7 and 7 square feet
d. 9x + 63 and 63 square feet

Answer 1

d. 9x + 63 and 63 square feet

Explanation:

Given

Original

`Length = x`

`Width = 9`

Extended

`Length = x + 7`

`Width = 9`

`Area = 9(x + 7)`

Required

Determine an expression and the value of the extended area

First, we calculate the area of the original desk

`A_1 = x * 9`

`A_1 = 9x`

From the given parameters, we have:

`Area = 9(x + 7)` --- area of the new surface

Open bracket

`Area = 9x + 63`

The area of the new surface is the summation of the area of the original desk and the area of the extended portion (E)

So:

`Area = A_1 + E`

Make E the subject

`E= Area - A_1`

`E= 9x + 63 - 9x`

`E= 63`

Hence, the area of the extended portion is 63