Question

the perimeter of the original square is eight inches more than the length of one side of the larger square. what is the length, in inches, of each side of the larger square? 2 1/3

Explanation:

Step1: Recall perimeter formula for square

The perimeter of a square with side - length $s$ is $P = 4s$. For the original square with side - length $x$, its perimeter is $P=4x$.

Step2: Set up the equation

We are given that the perimeter of the original square is eight inches more than the length of one side of the larger square. The side - length of the larger square is $x + 2$. So, the equation is $4x=(x + 2)+8$.

Step3: Solve the equation

First, simplify the right - hand side: $4x=x + 10$. Then, subtract $x$ from both sides: $4x−x=x + 10−x$, which gives $3x = 10$. Divide both sides by 3: $x=\frac{10}{3}$.

Step4: Find the side - length of the larger square

The side - length of the larger square is $x + 2$. Substitute $x=\frac{10}{3}$ into $x + 2$: $\frac{10}{3}+2=\frac{10}{3}+\frac{6}{3}=\frac{10 + 6}{3}=\frac{16}{3}=5\frac{1}{3}$.

Answer:

$\frac{16}{3}$