Question

a rectangular blanket for a child that measures 3 feet by 4 feet is made. a border that is exactly 6 square feet is to be created around the blanket. which two equations represent the required width of the border, $x$? a. $(3 + x)(4 + x)=18$ b. $(3 + 2x)(4 + 2x)=18$ c. $(3 + x)(4 + x)-3(4)=6$ d. $(3 + 2x)(4 + 2x)=6$ e. $(3 + 2x)(4 + 2x)-3(4)=6$

Explanation:

Step1: Find the area of the original blanket

The area of the original rectangular blanket with length $l = 4$ feet and width $w=3$ feet is $A_{0}=3\times4 = 12$ square - feet.

Step2: Find the area of the blanket with the border

The area of the border is 6 square - feet. So the area of the blanket with the border is $A=12 + 6=18$ square - feet.

Step3: Determine the dimensions of the blanket with the border

If the width of the border is $x$ feet, then the length of the blanket with the border is $4 + 2x$ feet and the width is $3+2x$ feet. The area of the blanket with the border is $(3 + 2x)(4 + 2x)$.

Step4: Set up the equation

Since the area of the blanket with the border is 18 square - feet, we have the equation $(3 + 2x)(4 + 2x)=18$. Also, we can think of it as the area of the blanket with the border minus the area of the original blanket equals the area of the border. So $(3 + 2x)(4 + 2x)-3\times4 = 6$.

Answer:

B. $(3 + 2x)(4 + 2x)=18$
E. $(3 + 2x)(4 + 2x)-3\times4 = 6$