SOLUTION: the premiter of rectangle ABCD is 20 inches. find the least value, in inches, of diagonal AC. answers must be in exact form.

Click here to see ALL problems on Parallelograms

Question 1013245: the premiter of rectangle ABCD is 20 inches. find the least value, in inches, of diagonal AC. answers must be in exact form.
Found 2 solutions by stanbon, addingup:
Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
the perimiter of rectangle ABCD is 20 inches. find the least value, in inches, of diagonal AC. answers must be in exact form.
----
P = 2(L + W)
------
20 = 2(L+W)
L+W = 10
------
Diam = sqrt[L^2 + W^2)
-----
Substitute for "L" to get:
D = sqrt[(10-W)^2 + W^2]
D = sqrt[2W^2 - 20W + 100]
-------------------
Take the derivative to get:
D' = (1/2)(4W-20)/sqrt(2W^2-20W+100)
---
Solve:: 2W-10 = 0
W = 5
Then L = 5
-----
Ans: D = sqrt[5^2 + 5^2] = sqrt(2*25) = 5sqrt(2)
-------------
Cheers,
Stan H.
-------------

Answer by addingup(3677) (Show Source):
You can put this solution on YOUR website!
20/4 = 5
5^2+5^2 = 50
sqrt50= 7.07 is the least-value diagonal