Question

lmnp is a rectangle. find the value of x and the length of each diagonal. ln = 5x + 11 and mp = 7x - 5

Explanation:

Step1: Set diagonals equal

In a rectangle, diagonals are equal: $5x + 11 = 7x - 5$

Step2: Solve for x

Rearrange terms: $11 + 5 = 7x - 5x$ → $16 = 2x$ → $x = 8$

Step3: Calculate diagonal length

Substitute $x=8$ into $5x+11$: $5(8)+11=40+11=51$

Answer:

x = 8
Length of each diagonal = 51