Question

the perimeter of the rectangle below is 164 units. what is the value of x?

a. x = 24.7
b. x = 11
d. x = 15
c. x = 4.1

Explanation:

Step1: Write 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, \(l=4x + 16\) and \(w = 2x\), and \(P=164\). So, \(164=2((4x + 16)+2x)\).

Step2: Simplify the equation

First, divide both sides of the equation \(164=2((4x + 16)+2x)\) by \(2\). We get \(82=(4x + 16)+2x\). Then combine like - terms: \(82=6x + 16\).

Step3: Solve for \(x\)

Subtract \(16\) from both sides: \(82-16=6x\), so \(66 = 6x\). Then divide both sides by \(6\): \(x=\frac{66}{6}=11\).

Answer:

B. \(x = 11\)