Question

lmnp is a rectangle. find the value of x and the length of each diagonal.
ln = 3x + 44 and mp = 9x - 4
x = \square

Explanation:

Step1: Set diagonals equal

In a rectangle, diagonals are congruent: $3x + 44 = 9x - 4$

Step2: Solve for x

Subtract $3x$: $44 = 6x - 4$; add 4: $48 = 6x$; divide by 6: $x = 8$

Step3: Calculate diagonal length

Substitute $x=8$ into $3x + 44$: $3(8) + 44 = 24 + 44 = 68$

Answer:

x = 8, Length of each diagonal = 68