Question

Question 10 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 equations represent the required width of the border, X? Select all that apply.

Answer 1

ANSWER

The equations that apply are: B and D

EXPLANATION

The blanket with the border is:

The area of the border is the total area of the blue rectangle minus the area of the black rectangle - which is the blanket.

The width of the blue rectangle is: 3 + 2x - because we have a border with x width on both sides.

The length of the blue rectangle is: 4 + 2x.

The area of the blue rectangle is:

$(3+2x)(4+2x)$

This area minus the area of the black rectangle - which is 3(4) must be 6 square feet - the area of the border:

$(3+2x)(4+2x)-3(4)=6$

If we take the area of the black rectangle to the other side of the equality:

$\begin{gathered} (3+2x)(4+2x)-12=6 \\ (3+2x)(4+2x)=6+12 \\ (3+2x)(4+2x)=18 \end{gathered}$