LMNP is a rectangle. Find the value of x and the length of each diagonal. LN = 7x+9 and MP=9x-9

see explanation

Step-by-step explanation:

The diagonals of a rectangle are congruent, thus

MP = LN, substitute values

9x - 9 = 7x + 9 (subtract 7x from both sides)

2x - 9 = 9 (add 9 to both sides)

2x = 18 (divide both sides by 2)

x = 9

LN = 7x + 9 = (7 * 9) + 9 = 63 + 9 = 72

MP = 9x - 9 = (9 * 9) - 9 = 81 - 9 = 72