Question

lmnp is a rectangle. find the value of x and the length of each diagonal.
ln = 5x + 11 and mp = 7x - 5
x = 8
ln = 51
mp = \square

Explanation:

Step1: Use rectangle diagonal property

Diagonals of a rectangle are equal, so $5x + 11 = 7x - 5$.

Step2: Solve for x

Rearrange: $11 + 5 = 7x - 5x \Rightarrow 16 = 2x \Rightarrow x = 8$.

Step3: Calculate MP length

Substitute $x=8$ into $MP=7x - 5$: $7(8) - 5 = 56 - 5 = 51$.

Answer:

51