Question

use the given figure to find an expression for the perimeter of the shape. simplify the expression if possible. note: perimeter is the sum of the lengths of t perimeter of a rectangle 2y + 4 x + 7

Explanation:

Step1: Recall the formula for the perimeter of a rectangle

The formula for the perimeter \(P\) of a rectangle is \(P = 2(l + w)\), where \(l\) is the length and \(w\) is the width. Here, \(l=x + 7\) and \(w=2y+4\).

Step2: Substitute the values of length and width into the formula

Substitute \(l=x + 7\) and \(w=2y+4\) into \(P = 2(l + w)\), we get \(P=2((x + 7)+(2y+4))\).

Step3: Simplify the expression inside the parentheses

First, simplify \((x + 7)+(2y+4)\) using the commutative and associative properties of addition: \((x + 7)+(2y+4)=x+2y+(7 + 4)=x+2y + 11\).

Step4: Distribute the 2

Then, distribute the 2 in \(P = 2(x+2y + 11)\). Using the distributive property \(a(b + c+d)=ab+ac+ad\) (here \(a = 2\), \(b=x\), \(c = 2y\), \(d = 11\)), we have \(P=2x+4y+22\).

Answer:

\(2x + 4y+22\)