Question

view submission
calculator
a rectangle has a perimeter of 48 ft. the length and width are scaled by a factor of 1.5.
what is the perimeter of the resulting rectangle?
enter your answer in the box.
ft

Explanation:

Step1: Recall the formula for the perimeter of a rectangle

The perimeter of a rectangle is \(P = 2(l + w)\), where \(l\) is the length and \(w\) is the width.

Step2: Analyze the effect of scaling

If the length and width are scaled by a factor of \(k = 1.5\), the new length \(l'\) and new width \(w'\) are \(l'=1.5l\) and \(w' = 1.5w\). The new perimeter \(P'=2(l' + w')=2(1.5l + 1.5w)\).
Using the distributive property \(a(b + c)=ab+ac\), we have \(P'=1.5\times2(l + w)\).
Since \(P = 2(l + w)=48\) ft, then \(P'=1.5\times P\).

Step3: Calculate the new perimeter

Substitute \(P = 48\) into the equation \(P'=1.5\times P\). So \(P'=1.5\times48 = 72\) ft.

Answer:

72