Question

the perimeter of the rectangle below is 88 units. find the length of side \\( \overline { q r } \\). write your answer without variables.

Explanation:

Step1: Use 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, \(l = 4x\), \(w=3x + 2\), and \(P = 88\). So, \(88=2(4x+(3x + 2))\).

Step2: Simplify the equation

First, simplify inside the parentheses: \(4x+(3x + 2)=7x + 2\). Then the equation becomes \(88 = 2(7x + 2)\). Divide both sides by 2: \(\frac{88}{2}=7x + 2\), so \(44=7x + 2\).

Step3: Solve for \(x\)

Subtract 2 from both sides: \(44−2=7x\), which gives \(42 = 7x\). Then divide both sides by 7: \(x=\frac{42}{7}=6\).

Step4: Find the length of \(QR\)

Since \(QR = 4x\), substitute \(x = 6\) into \(4x\). So \(QR=4\times6 = 24\).

Answer:

24