Question

if lmno is a rectangle, and mo = 36, what is the length of \\(\overline{np}\\) ?

a. 22
b. 18
c. 36
d. 72
e. 10
f. cannot be determined

Explanation:

Step1: Recall rectangle diagonals property

In a rectangle, the diagonals are equal in length and bisect each other. So, diagonals \( MO \) and \( LN \) are equal, and point \( P \) (the intersection of diagonals) bisects both diagonals.

Step2: Analyze the length of \( \overline{NP} \)

Given \( MO = 36 \), since diagonals in a rectangle bisect each other, \( NP=\frac{1}{2}LN \). But \( LN = MO = 36 \) (diagonals of a rectangle are equal). So, \( NP=\frac{36}{2}=18 \).

Answer:

B. 18