Question

1. a rectangle has a perimeter of 76 cm. the length measures (x + 4). the width measures (x+2). what is the value of x, in centimeters?

Explanation:

Step1: Use the perimeter formula for a rectangle

The perimeter formula for a rectangle is \(P = 2(l + w)\), where \(P\) is the perimeter, \(l\) is the length, and \(w\) is the width. Given \(P=76\), \(l=(x + 4)\), and \(w=(x + 2)\), we substitute these into the formula:
\(76=2((x + 4)+(x + 2))\)

Step2: Simplify the equation

First, simplify the expression inside the parentheses: \((x + 4)+(x + 2)=2x+6\). So the equation becomes \(76 = 2(2x + 6)\).
Then, distribute the 2: \(76=4x+12\).

Step3: Solve for \(x\)

Subtract 12 from both sides: \(76-12 = 4x+12-12\), which gives \(64 = 4x\).
Divide both sides by 4: \(\frac{64}{4}=\frac{4x}{4}\), so \(x = 16\).

Answer:

\(x = 16\)