Question

A piece of wire 7 m long is cut into two pieces. One piece is bent into a square and the other is bent into an equilateral triangle.

How much wire should be used for the square in order to minimize the total area?

I have already tried lots of answers but none of them are right.. only one chance left..!!!!

Answer 1

i am going to guess at 0 for the square, but let me do some calculation since you only have one chance

Answer 2

thankkkksss !!!

Answer 3

hmm maybe i am wrong.
take say \(x\) for the triangle, then the side of the triangle is \(\frac{x}{3}\) and the area is \(\frac{\sqrt{3}}{4}(\frac{x}{3})^2\)

Answer 4

that leaves \(7-x\) for the square, cut that in 4 parts and get an area of \((\frac{7-x}{4})^2\)

Answer 5

@Mertsj if i am messing up let me know

Answer 6

now we want to minimize
\[A=\frac{\sqrt{3}}{4}(\frac{x}{3})^2+(\frac{7-x}{4})^2\]

Answer 7

i would have thought we used it all for the triangle, but that is not the result i am getting.
am i doing something wrong? anyone?

Answer 8

I'm with you so far. Same thing I got. Just finish up. I got 3.04 for square

Answer 9

i think u r right -- for the expression of A

Answer 10

\[\frac{\sqrt{3}x^2}{36}+\frac{(x-7)^2}{16}\] take derivative set equal zero and solve or else since this is a poly of degree 2, expand this mess and find the vertex

Answer 11

oh damn damn damn
you want "how much for the square"!! so should have made \(x\) the amount used for the square

Answer 12

No. Easier the way you did it. Just get answer and subtract from 7

Answer 13

then
\[A=\frac{x^2}{4}=\frac{\sqrt{3}(7-x)^2}{36}\]

Answer 14

yeah i suppose you are right

Answer 15

\(7-3.95525=3.04475\)

Answer 16

here of course i cheat because i will be damned if i am going to try this will pencil and paper
http://www.wolframalpha.com/input/?i=sqrt%283%29x^2%2F36%2B%287-x%29^2%2F16

Answer 17

And if we pay attention to significant digits then 4 inches for triangle and 3 inches for square.

Answer 18

guess my intuition was totally wrong. i would have said minimize by using all on the triangle

Answer 19

hold on

A=x^2/4 =[(3)^(1/2)(7-x)^2]/36

why?

Answer 20

the answer is correct !!!!!!!!

Answer 21

Answers by Satellite...never fail.

Answer 22

thank you guys !

I follow you before you say "Then A=... "

Answer 23

@Mertsj haha :D