Question

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

Answer 1

see explanation

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