LMNP is a rectangle Find the value of x and the length of each diagonal. LN=5x+20 and MP=8x-4 x= square

To solve this problem, we need to use the properties of a rectangle and the given information.

Given:
- LMNP is a rectangle
- LN = 5x + 20
- MP = 8x - 4

In a rectangle, the diagonals are equal in length. Therefore, we can set the lengths of the diagonals equal to each other and solve for x.

Step 1: Set the lengths of the diagonals equal to each other.
LN = MP
5x + 20 = 8x - 4

Step 2: Solve for x.
5x + 20 = 8x - 4
20 + 4 = 8x - 5x
24 = 3x
x = 8

Step 3: Find the length of each diagonal.
LN = 5x + 20 = 5(8) + 20 = 40 + 20 = 60
MP = 8x - 4 = 8(8) - 4 = 64 - 4 = 60

Therefore, the value of x is 8, and the length of each diagonal is 60.