Question

the perimeter of the rectangle is 28 units. what is the value of w? 5 units 7 units 14 units 15 units

Explanation:

Step1: Recall the perimeter formula for a rectangle

The perimeter formula of a rectangle is \(P = 2(l + w)\), where \(l\) is the length and \(w\) is the width. Here, \(l=2w - 1\) and \(P = 28\). Substitute these into the formula: \(28=2((2w - 1)+w)\).

Step2: Simplify the equation

First, divide both sides of the equation \(28 = 2((2w - 1)+w)\) by 2: \(\frac{28}{2}=(2w - 1)+w\), which gives \(14=3w - 1\).

Step3: Solve for \(w\)

Add 1 to both sides of the equation \(14 = 3w-1\): \(14 + 1=3w\), so \(15 = 3w\). Then divide both sides by 3: \(w=\frac{15}{3}=5\).

Answer:

5 units