Question

1. the perimeter of a rectangle is 126 feet. the length of the rectangle is 8x and the width is (x + 9). find the value of x:

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.

Step2: Substitute the given values into the formula

We know that \(P=126\), \(l = 8x\), and \(w=x + 9\). So, \(126=2(8x+(x + 9))\).

Step3: Simplify the equation

First, simplify inside the parentheses: \(8x+(x + 9)=9x + 9\). Then the equation becomes \(126=2(9x + 9)\).
Divide both sides by \(2\): \(\frac{126}{2}=9x + 9\), which simplifies to \(63=9x + 9\).

Step4: Solve for \(x\)

Subtract \(9\) from both sides: \(63-9=9x\), so \(54 = 9x\).
Divide both sides by \(9\): \(x=\frac{54}{9}=5\).

Answer:

\(x = 5\)