Question

5 the perimeter of the rectangle below is 42 inches. find the value of x. 5x x - 3 47x - 126 show hint

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, \(l = 5x\) and \(w=x - 3\), and \(P = 42\). So, \(42=2(5x+(x - 3))\).

Step2: Simplify the equation inside the parentheses

First, simplify \(5x+(x - 3)\): \(5x+x - 3=6x - 3\). The equation becomes \(42 = 2(6x - 3)\).

Step3: Distribute the 2

Using the distributive property \(a(b + c)=ab+ac\) (here \(a = 2\), \(b = 6x\), \(c=-3\)), we get \(42=12x-6\).

Step4: Solve for \(x\)

Add 6 to both sides of the equation: \(42 + 6=12x-6 + 6\), which simplifies to \(48 = 12x\). Then divide both sides by 12: \(x=\frac{48}{12}\).

Answer:

\(x = 4\)