Question

1. a formula for the perimeter of a rectangle is (p = 2l+2w). a. solve the formula for (w). b. use the new formula to find the width (w) (in meters) of a rectangle with a perimeter of 7 meters and a length of 2.4 meters.

Explanation:

Step1: Isolate the term with \(w\)

Given \(P = 2l+2w\), subtract \(2l\) from both sides: \(P - 2l=2w\).

Step2: Solve for \(w\)

Divide both sides of the equation \(P - 2l = 2w\) by 2. So \(w=\frac{P - 2l}{2}\).

Step3: Substitute values

We are given \(P = 7\) meters and \(l = 2\) meters. Substitute into \(w=\frac{P - 2l}{2}\), we get \(w=\frac{7-2\times2}{2}\).

Step4: Calculate the value of \(w\)

First, calculate the numerator: \(7-2\times2=7 - 4=3\). Then \(w=\frac{3}{2}=1.5\) meters.

Answer:

a. \(w=\frac{P - 2l}{2}\)
b. \(1.5\) meters