Question

the perimeter of the rectangle below is 150 units. find the value of z.

3z + 3

4z + 2

z =

Explanation:

Step1: Write the formula for the perimeter of a rectangle

The perimeter \(P\) of a rectangle is given by \(P = 2(l + w)\), where \(l\) is the length and \(w\) is the width. Here, \(l=4z + 2\) and \(w = 3z+3\), and \(P = 150\). So, \(150=2((4z + 2)+(3z + 3))\).

Step2: Simplify the equation

First, simplify inside the parentheses: \((4z + 2)+(3z + 3)=7z + 5\). Then the equation becomes \(150=2(7z + 5)\). Distribute the 2: \(150 = 14z+10\).

Step3: Solve for \(z\)

Subtract 10 from both sides: \(150-10=14z\), so \(140 = 14z\). Divide both sides by 14: \(z=\frac{140}{14}\).

Answer:

\(z = 10\)