This problem is impossible.

[exitwound]

The area of an equilateral triangle is increasing at the rate of 4 in²/min. At what rate is one side increasing when the area is 16in²?

Been working on it for like 5 hours now. Can't figure it out. About to throw someone through a wall.

[masraum]

I assume you're in Calc and working with derivatives and related rates?

< EDIT >BLAH, BLAH, BLAH. THERE WAS A TYPO IN MY FIRST ANSWER. GIMME A MINUTE TO REWRITE IT.< /EDIT >

A great online resource for math, especially college (Algebra, Calc I/II/III and DE) is "Paul's online math notes" (apparently a professor at Lamar Univ in Texas)

Here's a link to his Calc I notes.
http://tutorial.math.lamar.edu/Classes/CalcI/CalcI.aspx

Here's his main site.
http://tutorial.math.lamar.edu/

[masraum]

< edit > I screwed up again, thanks dad911 < /edit >

This is more difficult, but it still works out the same way. Getting the measure of a side when the area is 16 is messier with the correct formula (assuming you can't use a calculator and give the answer in decimals).

16 = √3/4•s²

s = 8/fourth root of 3
s' = looking for
A = 16
A' = 4

A = √3/4•s²
A' = √3/2•ss'

s' = 2A'/(s•√3)

s' = 8/(8/(fourth root of 3)•√3)

Assuming I didn't screw up again....

s' = 1/fourth root of 3

Sheesh, I hope that's right, but having to use the fourth root would be unusual for most math classes

[Rick V]

Nerd.

[Cdnone1]

what masraum said
steve

[sammyg2]

Originally Posted by Cdnone1

what masraum said
steve

Damn, that was my line

[masraum]

Originally Posted by Rick V

Nerd.

Hahaha, yeah.

This is home



If I can't get the company to spring for a couple of better monitors (1280x1024 left and 1440x900 right) I'm going to have to buy my own.

Notice the titanium 911 con rod, G50.50 pinion (From Hank Watt's Green Monster), and 2.7L P&C (pen holder).

I need a Mg intake valve cover and standard steel rod. I also want to bring in my old fan and shroud. You can never be surrounded by enough greasy old car parts.

[dad911]

Originally Posted by masraum

.... Since they say "equilateral triangle" we know the b and h are equal ....

Equilateral is all 3 sides equal. Height is not equal to base......

area is represented as:



http://www.mathwords.com/a/area_equilateral_triangle.htm

[TheMentat]

how do you type that square root symbol?

[masraum]

Originally Posted by dad911

Equilateral is all 3 sides equal. Height is not equal to base......

area is represented as:



http://www.mathwords.com/a/area_equilateral_triangle.htm

Crap!

Hahahah, damn!

[masraum]

Originally Posted by TheMentat

how do you type that square root symbol?

hold down the key and type 251 on the number pad.

[dad911]

Originally Posted by masraum

hold down the key and type 251 on the number pad.

Nah, I cheated. Uploaded the graphic from the mathworlds site.

A few beers less, and I would try to figure out the answer, maybe tomorrow.... but then again, a few beers more, and I would have agreed with masraum(steve)

[exitwound]

Originally Posted by masraum

OK, I was correct about the beginning, and I suspect that's where you're getting hung up. Normally, the area of a triangle is ½bh. Since they say "equilateral triangle" we know the b and h are equal so Area of an equilateral triangle is ½s²

There will be 4 variables, A, A', s and s'.

A = given (16in²)
s = working backwards from 16in² gives 4√2
A' = 4 in²/min
s' = don't know, that's the problem.

A = ½s²
A'= ss'

s' = A'/s = 4/4√2 = 1/√2 = 2/√2

The side is increasing at 2/√2 in/min

Actually the answer is 1(3^1/4) in/minute.

• Yes, the area of the equilateral triangle is ½s².
• s=4√2
• dA/dt = 4 in²/min
• So if A=½s² , dA/dt = 2(½)s(ds/dt)
• simplify: dA/dt=s(ds/dt), 4=4√2(ds/dt),
• ds/dt = 1/√2 which is WRONG and why I can't figure out how to do this problem and want to stab someone in the throat.

Hmm that Area equation is probably where I was going wrong too.... WHY WAS GEOMETRY 17 YEARS AGO?!

[Eric Coffey]

This forum/thread may shed some light:
http://www.physicsforums.com/showthread.php?t=297625

[Rick V]

Dude that was your 911th post.

[exitwound]

Originally Posted by Eric Coffey

This forum/thread may shed some light:
http://www.physicsforums.com/showthread.php?t=297625

I first attempted using Pythagoreus but got stuck a hundred and twenty one different ways.

[dad911]

Ok, Use Heron's formula, (not Pythagorean) to get the area, and you will get the same area formula that I showed above. http://en.wikipedia.org/wiki/Heron%27s_formula

[RWebb]

Originally Posted by exitwound

The area of an equilateral triangle is increasing at the rate of 4 in²/min. At what rate is one side increasing when the area is 16in²?

Been working on it for like 5 hours now. Can't figure it out. About to throw someone through a wall.

1. rate of increase of side length is a function of rate of increase of area

2. area (per se) = 16

3. all sides equal ====> only need to know about any one side

you need the formula to derive the area from the length of a side

then rearrange to focus on side length

differentiate

if non-linear, evaluate the rate at #2 above

& you are done

go for a walk when frustrated

good luck and you can tell your prof. that I did NOT give you the answer.

[exitwound]

I KNOW the process. I can't do the math or put the picture together.

[exitwound]

Well, after doing it multiple times (obviously making stupid errors along the way), I think I got it.

A = (s²√3)/4

s= 8/(3^¼)

A'=(√3/4)(2s)(s')

4=(√3/4)(2)[8/(3^¼)](s')
2=(√3/4)(8/(3^¼)](s')
(8/√3)=[8/(3^¼)](s')
(8/(3^¼)) / (8√3) = s'
s' = 3^¼ / 3^ ½ = 3^(-¼)

s' comes out to be 1/(3^¼).