Question

1. higher order thinking a carpenter plans to extend the length of a rectangular desk by 7.25 feet. let x represent the desk’s original length. the expression 9(x + 7.25) represents the area of the desk’s surface, where 9 is the width, in feet, and (x + 7.25) represents the extended length, in feet, of the desk. the carpenter thinks that the area of the extended portion of the desk is 16.25 square feet. which choice below includes the expanded form of the area expression for the desk’s surface and the correct area of the extended portion of the desk’s surface? a (10x + 16.25) and 16.25 square feet b (9x + 65.25) and (9x) square feet c (9x + 7.25) and 7.25 square feet d (9x + 65.25) and 65.25 square feet

Explanation:

Step1: Expand the area expression

Using the distributive property \( a(b + c)=ab+ac \), for \( 9(x + 7.25) \), we have \( 9\times x+9\times7.25 \). Calculating \( 9\times7.25 = 65.25 \), so the expanded form is \( 9x + 65.25 \).

Step2: Find the area of the extended portion

The original area is \( 9x \) (when length is \( x \) and width is \( 9 \)), and the new area is \( 9x + 65.25 \). The extended area is the difference between new area and original area: \( (9x + 65.25)-9x=65.25 \) square feet.

Answer:

D. \( 9x + 65.25 \) and \( 65.25 \) square feet