Question

tina has two rectangular playpens to keep her new pet dogs. the first rectangle has a width of 6 feet and a length of x - 4 feet. the second rectangle has a width of 8 feet and a length of x + 2 feet. what is the sum of the two perimeters?

Explanation:

Step1: Find the perimeter formula for a rectangle

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

Step2: Calculate the perimeter of the first rectangle

For the first rectangle, \(w_1=6\) and \(l_1=x - 4\). Then \(P_1=2((x - 4)+6)=2(x + 2)=2x+4\).

Step3: Calculate the perimeter of the second rectangle

For the second rectangle, \(w_2 = 8\) and \(l_2=x + 2\). Then \(P_2=2((x + 2)+8)=2(x + 10)=2x+20\).

Step4: Find the sum of the two perimeters

\(P_{total}=P_1 + P_2=(2x + 4)+(2x+20)=4x + 24\).

Answer:

\(4x + 24\)