Question

the perimeter of the rectangle below is 164 units. what is the value of x? a. x = 24.7 b. x = 11 c. x = 4.1 d. x = 15

Explanation:

Step1: Recall the perimeter formula for a rectangle

The perimeter formula for 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 \(P=164\).
Substitute into the formula: \(164=2((4x + 16)+2x)\)

Step2: Simplify the equation

First, simplify the expression inside the parentheses: \((4x + 16)+2x=6x + 16\).
The equation becomes \(164 = 2(6x + 16)\).
Divide both sides by 2: \(\frac{164}{2}=6x + 16\), so \(82=6x + 16\).

Step3: Solve for \(x\)

Subtract 16 from both sides: \(82-16 = 6x\), which gives \(66 = 6x\).
Divide both sides by 6: \(x=\frac{66}{6}=11\).

Answer:

B. \(x = 11\)