Question

the rectangle pictured below has a perimeter of 83 inches. write an equation for th
x = type your answer...
12
4x + 2
2x + 8
5x + 6

Explanation:

Step1: Recall the formula for the perimeter of a rectangle

The perimeter \( P \) of a rectangle is \( P=\text{sum of all side lengths}\). So, \(P = 12+(4x + 2)+(5x + 6)+(2x + 8)\).

Step2: Simplify the left - hand side of the equation

Combine like terms:

$$
LATEXBLOCK0
$$

Since \(P = 83\), the equation is \(11x+28 = 83\).

Step3: Solve the equation for \(x\)

Subtract 28 from both sides: \(11x+28-28=83 - 28\), which gives \(11x=55\).
Divide both sides by 11: \(x=\frac{55}{11}\).

Answer:

\(x = 5\)