I have a parallelogram with sides AB and CD each 36' long and sides AC and BD each 22' long. Corner A to corner D is 43'2" long and corner B to corner C is 41'1" long. How far will corner C have to travel for this parallelogram to become a rectangle?
To find the distance corner C will have to travel for the parallelogram to become a rectangle, we need to calculate the difference between the existing diagonal BD (41'1") and the desired diagonal AC (36' + 22' = 58').
Let's first find the length of diagonal BD:
Using the Pythagorean theorem, we can find the length of diagonal BD.
BD^2 = AB^2 + AD^2
BD^2 = 36^2 + (43'2")^2
To calculate BD, convert 43'2" to feet. Since there are 12 inches in a foot, the total inches would be (43 * 12) + 2.
BD^2 = 36^2 + (43 * 12 + 2)^2
Now, simplify the equation:
BD^2 = 36^2 + (516 + 2)^2
BD^2 = 1296 + (518)^2
BD^2 = 1296 + 268,324
BD^2 = 269,620
Taking the square root of both sides:
BD ≈ √269,620
BD ≈ 519.47 feet (rounded to two decimal places)
Next, we need to find the difference between the desired diagonal AC (58') and the length of diagonal BD:
58' - BD ≈ 58' - 519.47 ≈ -461.47 feet
The negative indicates that corner C needs to move in the opposite direction of diagonal BD. Therefore, corner C will have to travel approximately 461.47 feet to convert the parallelogram into a rectangle.