Question

the perimeter of a rectangle is 48 centimeters. the relationship between the length, the width, and the perimeter of the rectangle can be described with the equation 2·length + 2·width = 48.
find the length, in centimeters, if the width is:
10 centimeters
3.6 centimeters
w centimeters

Explanation:

Step1: Substitute width value into equation

For width \( w = 10\) cm, substitute into \(2l+2w = 48\). We get \(2l+2\times10=48\), which simplifies to \(2l + 20=48\).

Step2: Solve for \(l\)

Subtract 20 from both sides: \(2l=48 - 20\), so \(2l=28\). Then divide both sides by 2: \(l=\frac{28}{2}=14\).

Step3: Substitute width value into equation (for \(w = 3.6\) cm)

Substitute \(w = 3.6\) into \(2l+2w = 48\). We have \(2l+2\times3.6=48\), which simplifies to \(2l+7.2 = 48\).

Step4: Solve for \(l\)

Subtract 7.2 from both sides: \(2l=48 - 7.2\), so \(2l = 40.8\). Then divide both sides by 2: \(l=\frac{40.8}{2}=20.4\).

Step5: Substitute width value into equation (for \(w\) cm)

Substitute \(w\) into \(2l+2w = 48\). We get \(2l+2w=48\).

Step6: Solve for \(l\)

Subtract \(2w\) from both sides: \(2l=48 - 2w\). Then divide both sides by 2: \(l=\frac{48 - 2w}{2}=24 - w\).

Answer:

• When width \(w = 10\) cm, length \(l = 14\) cm.
• When width \(w = 3.6\) cm, length \(l = 20.4\) cm.
• When width \(w\) cm, length \(l=(24 - w)\) cm.