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

`mn=5`

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 √(25)`

`mn=\pm 5`

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