LMNP is a rectangle. Find the value of x and the length of each diagonal.

LN = 6x + 1 and MP = 9x-5

The given rectangle's diagonals are equal in length and is equal to 13 units.

Step-by-step explanation:

Step 1:

Given

LMNP is a rectangle.

LN = 6 x + 1

MP = 9 x - 5

We need to find length of rectangle's diagonals

Step 2:

The rectangle's diagonals are equal in length.

Here we have LN and MP as the given rectangle's diagonals

So LN = MP

=> 9x - 5 = 6x + 1

=> 9x-6x = 1+5

=> 3x = 6

=> x = 2

Step 3:

So LN = 6x + 1 = 6 (2) + 1 = 13

MP 9x - 5 = 9 (2) - 5 = 13

Step 4:

Answer:

The given rectangle's diagonals are equal in length and is equal to 13 units.