Question

the perimeter of the rectangle below is 148 units. find the length of side \overline{vw}. write your answer without variables.

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, \(l = 5x\), \(w=4x + 2\), and \(P = 148\). So, \(148=2(5x+(4x + 2))\).

Step2: Simplify the equation

First, simplify the expression inside the parentheses: \(5x+(4x + 2)=9x + 2\). Then the equation becomes \(148 = 2(9x + 2)\). Divide both sides by 2: \(\frac{148}{2}=9x + 2\), which simplifies to \(74=9x + 2\).

Step3: Solve for \(x\)

Subtract 2 from both sides: \(74−2 = 9x\), so \(72=9x\). Then divide both sides by 9: \(x=\frac{72}{9}=8\).

Step4: Find the length of \(VW\)

Since \(VW = 4x + 2\), substitute \(x = 8\) into the expression. \(VW=4\times8+2=32 + 2=34\).

Answer:

\(34\)