Question

given the rectangle to the right, express the perimeter as an algebraic expression containing the variable x. the perimeter is (simplify your answer cubic feet. square feet. feet.

Explanation:

Step1: Recall the perimeter formula for a rectangle

The perimeter formula for a rectangle is \(P = 2l+2w\), where \(l\) is the length and \(w\) is the width. Here, \(l = 4x\) and \(w=(3x - 2)\).
So, \(P=2\times(4x)+2\times(3x - 2)\).

Step2: Expand the expression

Using the distributive property \(a(b + c)=ab+ac\), we have:
\(2\times(4x)=8x\) and \(2\times(3x - 2)=6x-4\).
Then \(P = 8x+6x - 4\).

Step3: Combine like - terms

Combining the \(x\) terms (\(8x+6x=(8 + 6)x = 14x\)), we get \(P=14x-4\).

Answer:

The perimeter is \(14x - 4\) feet.