If m>3 , n>5 , k<6, find the minimum integer value of 3m+5n-2k

Since m > 3 and n > 5, suppose we take m and n to be the smallest possible integers, m = 4 and n = 6. Then

3m + 5n - 2k = 42 - 2k

which is minimized by the largest value that k can take, k = 5. So the minimum value of 3m + 5n - 2k would be 32.

The length of each side of each leaf is about 5.7.

I assume the the side you are looking for is the outside diagonal side.

To find this, you can use the Pythagorean Theorem for half the distance.

2^2 + 2^2 = c^2
4 + 4 = c^2
8 = c^2
2.828 = c

Now, multiply this by 2 because we only found half of the complete side.
The length is about 5.7 units.