4th grade algebra: There are two squares. The length of the side of the larger square is three times the length of a side of the smaller square. If the larger s

Question

There are two squares. The length of the side of the larger square is three times the length of a side of the smaller square. If the larger square's perimeter is 48 inches more than the smaller square's perimeter, what is the length of one side of the smaller square?

Answer 1

With these types of questions, it's always a good idea to actually draw out a big square and a small square to visualize what's going on, which I unfortunately can't do here.

 

You want to define the side length of each square in terms of x by setting one to x. Setting the smaller length to x will avoid the use of fractions in your equation.

 

smaller side length = x;

larger side length = 3x; The length of the larger square is three times the length of the smaller square.

 

Next, you need to define the perimeters, which is the sum of all the sides of the squares.

 

small square perimeter = 4 times x = 4x;

large square perimeter = 4 times 3x = 12x;

 

Now, set up the equation to solve.

 

12x = 4x + 48

 

The larger square's perimeter is 48 inches more than the smaller square's perimeter.

 

Solving the equation gives x = 6. We defined x in the beginning to represent the side length of the small square, so the answer is 6 inches.