Question

solving equations using perimeter & area of rectangles quiz (8.bc)
the perimeter and area of the rectangle below is the same. if the width is 10 in, which equation is correct to find the length of the rectangle?
10 in
10 + 10+l + l = 2l
10 + l = 2l
10 + 10+l + l = 10l
10 + l = 10l

Explanation:

Step1: Recall perimeter formula

The perimeter $P$ of a rectangle with length $L$ and width $w$ is $P = 2w+2L$. Given $w = 10$, then $P=10 + 10+L + L$.

Step2: Recall area formula

The area $A$ of a rectangle with length $L$ and width $w$ is $A=wL$. Given $w = 10$, then $A = 10L$.

Step3: Set perimeter equal to area

Since $P = A$, we have $10 + 10+L + L=10L$.

Answer:

$10 + 10+L + L=10L$