SOLUTION: Find the smallest possible length for a diagonal of a rectangle with a perimeter of 10 feet. Is there a second way of solving this problem? If so, please show

Question 708791: Find the smallest possible length for a diagonal of a rectangle with a perimeter of 10 feet.
Is there a second way of solving this problem? If so, please show
Answer by josgarithmetic(39620) (Show Source): You can put this solution on YOUR website!
A semester-1 Calculus problem.

x, length in one direction
y, length in other direction
h, length of diagonal

perimeter is 2(x+y)
perimeter is a constant, 10 feet:
IDEA: Use perimeter equation and solve it for y. Substitute this into the diagonal equation.

This last formula or function, you want to see if you can find the minimum, if possible. Find the derivative and see about setting it equal to zero and this might help. (The function does in fact have a minimum.)
RELATED QUESTIONS
A rectangle with a perimeter of 98 feet has a length 31 feet longer than its width. What (answered by josgarithmetic)

what is the least possible diagonal of a rectangle with a perimeter of... (answered by richard1234)

Find the length of a diagonal of a square enclosure with a perimeter of 16 feet (answered by Alan3354)

A rectangle has a diagonal of length 10 and one side of length 6 find the perimeter of... (answered by Alan3354)

what is the diagonal length of a rectangle 10 feet by 12 feet (answered by checkley77)

If the diagonal of a rectangle has a length 7 feet and the rectangles area is 16 square... (answered by ankor@dixie-net.com,josgarithmetic,MathTherapy)

The question is find the amount of fencing in linear feet needed for the perimeter of a... (answered by swincher4391)

The perimeter of a rectangle is 34 feet, the diagonal is 13 feet. What is the length and... (answered by edjones)

The perimeter of a rectangle is 32m. Find the dimensions for which the diagonal is as... (answered by Fombitz)