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The sum of the perimeters of an equilateral triangle and square is 10. Find the dimensions of the triangle and the square that produce a minimum total area.

Thanks for any help

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- Thread starter mattxr250
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- #1

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The sum of the perimeters of an equilateral triangle and square is 10. Find the dimensions of the triangle and the square that produce a minimum total area.

Thanks for any help

- #2

EnumaElish

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So you have 3L + 4L = 7L = 10, so L = 10/7, is that right? Or is it more complicated?

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Well it could be 3L + 4W = 10. Are the sides of the triangle the same as the square?

- #4

EnumaElish

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Let's see how mattxr250 thinks it is. mattxr250 are you there?

- #5

HallsofIvy

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mattxr250, as apmcavoy says, the total perimeter would be 3L + 4W = 10 (I assume he means L as the length of a side of the triangle and W as the side of the square. The area of the square would be W

- #6

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L = (10-4W)/3...

so does this make sense for the perimeter?

3[(10-4W)/3] + 4W = 10...after that i'm lost, lol...any more help?

- #7

EnumaElish

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You have two unknowns L and W but one equation. Can you determine 2 unknowns from a single equation?mattxr250 said:so does this make sense for the perimeter?

3[(10-4W)/3] + 4W = 10...

The thread title said calc optimization, so where do you think is the calculus or the optimization part? Okay, I see that you said area needs to be minimized. So how do you write the total area in terms of L and W?

- #8

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to get the optimization part you need the equations for the area, differentiate them, and then find the min of f '(x), but I dont know how...help??

- #9

EnumaElish

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- #10

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what do I differentiate?? the two forumlas for area?

- #11

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[(3^(1/2))/4](L^2)...

i really need help guys...any suggestions?

- #12

EnumaElish

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