Question

question 4, presenter: a rectangle is 5 inches long and 2x inches wide. the value of the perimeter (in inches) is equal to the value of the area (in square inches). find x.

Explanation:

Step1: Write the formula for perimeter and area

Perimeter of rectangle \(P = 2(l + w)\), where \(l = 5\) and \(w=2x\), so \(P=2(5 + 2x)=10 + 4x\).
Area of rectangle \(A=l\times w\), so \(A = 5\times2x=10x\).

Step2: Set up the equation

Since \(P = A\), we have \(10+4x=10x\).

Step3: Solve the equation

Subtract \(4x\) from both sides: \(10=10x - 4x\).
Simplify: \(10 = 6x\).
Divide both sides by \(6\): \(x=\frac{10}{6}=\frac{5}{3}\).

Answer:

\(\frac{5}{3}\)