A lawn has area of 64 sq meters. A straight rope is strung from one corner of the rectangle to the midpoint of one of the two more distant sides of the lawn. What is the minimum possible length of this rope?
A. 4 m
B. 8 m
C. 16 m
D. 32 m

Question

yuki · Answer

easy peasy

yuki · Answer

if you let x be one side, then 32-x is the other side

yuki · Answer

ops, sorry not 32-x

it is actually 64/x

yuki · Answer

then the midpoint of one side will be located at
32/x units from the other corner

yuki · Answer

so using the Pythagorean theorem, we can see that

$$x^2 + ({32 \over x})^2 $$

is the length of the rope

yuki · Answer

so what you want to do is to minimize this length

yuki · Answer

once you take the derivative of this function and let it = 0,
you should find an x that minimize it.

yuki · Answer

does that help ?

radar · Answer

Something seems askew with this solution.  $$x ^{2}+(32x ^{-1})^{2}$$being equal to the length as stated above does not seem complete.  Wouldn't that be in a radical other the square root of that be the length of the rope??