Question

if the difference in the side lengths of two squares is 10, and the sum of the side length is 18, what are the side lengths?

Answer 1

The side length of the smaller square is 4 units, and the side length of the larger square is 14 units.

Step-by-step explanation:

The problem states that the difference in the side lengths of two squares is 10 and the sum of the side lengths is 18. Let's assume x represents the side length of the smaller square.

The side length of the larger square would then be x + 10.

Using the information given, we can set up the equation: x + (x + 10) = 18. Solving for x, we find that the side length of the smaller square is 4 units, and the side length of the larger square is 14 units.

Answer 2

Set up the system of equations described in the question, and add the equations:


`x-y=10`

`+(x+y=18)`
________________

`\hspace*{1em} 2x \enspace \enspace \enspace =28 \\ewline \hspace*{1em} \enspace x \enspace \enspace \enspace =14`

Now that we have x=14, the other side length can be solved by substituting 14 into either equation to get y=4.

The side length of one square is 14. The side length of the other is 4.