Question

Consider rectangle abcd (not shown) with ab=8 and bc=6. if m and n are the midpoints of sides ab¯¯¯¯¯ and bc¯¯¯¯¯ respectively, find mn.

Answer 1

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 2

Answer:

$mn=5$

Step-by-step explanation:

Please find that attachment.

We have been given that in rectangle abcd, $ab=8$ and $bc=6$. 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.

$mn^2=mb^2+bn^2$

$mn^2=4^2+3^2$

$mn^2=16+9$

$mn^2=25$

Upon taking square root of both sides, we will get:

$mn=\pm \sqrt{25}$

$mn=\pm 5$

Since length cannot be negative, therefore, the length of mn is 5 units.