Question

1. consider the figure shown. does each expression represent the perimeter of the figure? choose yes or no.

2(2x + 3y)
x + x + x + x + 3y
4(x + y) + 2y
x + x + x + x + 6y
2(x + 3y)
4x + 3y

Explanation:

Step1: Calculate the perimeter of the figure

The perimeter of a figure is the sum of all its side lengths.
The vertical sides: \(x + x+x + x=4x\)
The horizontal sides: \(y + y+3y + y=6y\)
So the perimeter \(P = 4x+6y\)

Step2: Simplify each given expression

• For \(2(2x + 3y)\):

Using the distributive property \(a(b + c)=ab+ac\), we have \(2(2x+3y)=4x + 6y\)

• For \(x + x+x + x+3y\):

\(x + x+x + x+3y=4x+3y\)

• For \(4(x + y)+2y\):

First, use the distributive property: \(4(x + y)=4x+4y\), then \(4(x + y)+2y=4x+4y + 2y=4x+6y\)

• For \(x + x+x + x+6y\):

\(x + x+x + x+6y=4x+6y\)

• For \(2(x + 3y)\):

Using the distributive property: \(2(x + 3y)=2x+6y\)

• For \(4x + 3y\):

It is \(4x+3y\)

Answer:

Expression	Yes	No
\(x + x+x + x+3y\)		Yes
\(4(x + y)+2y\)	Yes
\(x + x+x + x+6y\)	Yes
\(2(x + 3y)\)		Yes
\(4x + 3y\)		Yes