Because M is a midpoint of AB, |MB| = 4,
N is a midpoint of BC, |BN|=3.
From the picture we see that MB and BN are the legs of the triangle MBN, where MN is a hypotenuse.
Using Pythagorean theorem
MN²=MB²+BN²
MN² = 4² + 3² = 25
|MN| = 5
Answer is |MN| = 5
Answer:
[tex]mn=5[/tex]
Step-by-step explanation:
Please find that attachment.
We have been given that in rectangle abcd, [tex]ab=8[/tex] and [tex]bc=6[/tex]. We are also told that m and n are the midpoints of sides ab and bc respectively.
Since m is point of ab, so am and mb will be 4 units each. Similarly, an and nc will be 3 units each.
When we will join a line connecting m and n, it will be hypotenuse of a right triangle mbn.
Now, we will use Pythagoras theorem to solve for mn.
[tex]mn^2=mb^2+bn^2[/tex]
[tex]mn^2=4^2+3^2[/tex]
[tex]mn^2=16+9[/tex]
[tex]mn^2=25[/tex]
Upon taking square root of both sides, we will get:
[tex]mn=\pm \sqrt{25}[/tex]
[tex]mn=\pm 5[/tex]
Since length cannot be negative, therefore, the length of mn is 5 units.
