The lengths of two adjacent sides of a square are represented by 5x+11 and 7x-3. What is the perimeter of the square?
5x + 11 = 7x + 3
11 - 3 = 7x - 5x
8 = 2x
4 = x
P = 4s
To find the perimeter of a square, we need to add up the lengths of all four sides. In this case, we are given the lengths of two adjacent sides of the square as 5x+11 and 7x-3.
To calculate the perimeter of the square, we need to find the lengths of the other two sides as well. Since a square has equal sides, any two adjacent sides will have the same length.
So, let's equate the lengths of the two given sides:
5x+11 = 7x-3
Now, we can solve this equation to find the value of x.
First, let's subtract 5x from both sides:
11 = 2x - 3
Next, let's add 3 to both sides:
14 = 2x
Finally, dividing both sides by 2:
x = 7
Now that we have found the value of x, we can substitute it back into either of the original expressions to find the lengths of the sides.
For example, substituting x = 7 into 5x+11:
5(7) + 11 = 35 + 11 = 46
Therefore, the length of each side of the square is 46.
To find the perimeter, we multiply the length of one side by 4 (since a square has four equal sides):
Perimeter = 4 * 46 = 184
Therefore, the perimeter of the square is 184 units.