The numbers 1, 2, ... ,10 are to be entered into the 10 boxes shown below, so that each number is used exactly once: P = (\square + \square + \square + \square + \square)(\square + \square + \square + \square + \square). What is the maximum value of P? What is the minimum value of P?

Maximum: 756

Minimum: 600

Step-by-step explanation:

A square is the shape that has the maximum area out of all possible rectangles of a given perimeter. This means that to create the maximum value of P, you will want the two parentheses to be as close in value as possible, and to create the minimum value, for them to have the biggest difference. 1+2+3...+10=55, which is not even, but can be divided as closely as possible into 27 and 28, which have a product of 756. This can be done in this problem in several ways, one of which is:

(1+3+5+8+10)(2+4+6+7+9)

For the minimum, the largest difference can be made when one term is full of the smallest numbers, and the other is full of the largest, or:

(1+2+3+4+5)(6+7+8+9+10)=600

Hope this helps!

the smallest possible measurement of the width is 14 feet

step-by-step explanation:

let's assume length of parallelogram is 'l'

width of parallelogram is 'w'

the perimeter of a parallelogram must be no less than 40 feet

so, we get

we are given

length of parallelogram is 6 feet

so,

l=6

we can plug it

now, we can solve for w

subtract both sides by 12

divide both sides by 2

and we get

so,

the smallest possible measurement of the width is 14 feet