Answer:
![mn=5](https://tex.z-dn.net/?f=mn%3D5)
Step-by-step explanation:
Please find that attachment.
We have been given that in rectangle abcd,
and
. 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.
![mn^2=mb^2+bn^2](https://tex.z-dn.net/?f=mn%5E2%3Dmb%5E2%2Bbn%5E2)
![mn^2=4^2+3^2](https://tex.z-dn.net/?f=mn%5E2%3D4%5E2%2B3%5E2)
![mn^2=16+9](https://tex.z-dn.net/?f=mn%5E2%3D16%2B9)
![mn^2=25](https://tex.z-dn.net/?f=mn%5E2%3D25)
Upon taking square root of both sides, we will get:
![mn=\pm \sqrt{25}](https://tex.z-dn.net/?f=mn%3D%5Cpm%20%5Csqrt%7B25%7D)
![mn=\pm 5](https://tex.z-dn.net/?f=mn%3D%5Cpm%205)
Since length cannot be negative, therefore, the length of mn is 5 units.