Answer:
[tex]MN = \sqrt{14[/tex]
Step-by-step explanation:
Given
[tex]NO = 12[/tex]
[tex]OP = 2.5[/tex]
[tex]OQ = 4.5[/tex]
Required
Find MN
First, we calculate QP using Pythagoras theorem
[tex]OQ^2 = OP^2 + QP^2[/tex]
[tex]4.5^2 = 2.5^2 + QP^2[/tex]
[tex]20.25 = 6.25 + QP^2[/tex]
Collect like terms
[tex]QP^2 = 20.25 - 6.25[/tex]
[tex]QP^2 = 14[/tex]
Take square roots
[tex]QP = \sqrt{14[/tex]
To solve MN, we have:
[tex]MN = OP[/tex]
So:
[tex]MN = \sqrt{14[/tex]
