The length of a side of a square is fifteen less than four times the length of a side of a second square. The perimeter of the two squares differ by 24 inches. Find in inches, the length of a side of the smaller square. [ Only an algebraic solution will be accepted ]
Try this one yourself by following a similar argument and solution like I just showed you in your previous post.
Hint: let x be the side of the first square and let y be the side of the second square.
Now express the English statements with algebraic equivalents.
To solve this problem algebraically, let's denote the length of a side of the larger square as "x".
According to the problem, the length of a side of the smaller square is fifteen less than four times the length of a side of the larger square. So, the length of a side of the smaller square can be expressed as 4x - 15.
The perimeter of a square is given by the formula P = 4s, where P is the perimeter and s is the length of a side.
The problem states that the perimeter of the two squares differs by 24 inches. Hence, we can write the equation as:
4x - 15 + 4x - 15 + 24 = 4x + 4x
Now, let's solve this equation step by step:
Combining like terms:
8x - 6 + 24 = 8x
Simplifying:
8x + 18 = 8x
Subtracting 8x from both sides:
18 = 0
Since we reached an invalid statement, this means there is no solution to the equation. Therefore, there is no value for the length of a side of the smaller square that satisfies the given conditions.