Four math questions for ye!

Wrappin up my math hw, but Im short on time for bday celebrations. Here's where I be stumped~

A triangle is equilateral if it has three equal sides. The triangle in the figure is equilateral with each side of length 2x. Find the ratio of the height to a side.

multiply

this is 2 (SRT) 14 - 14, right?

multiply

Rationalize the denominator in the following.

thanks!!

Last edit: 2008-04-19 06:23:07

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ieatkids5 United States. April 19 2008 06:28. Posts 4381

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problem 1
if you cut that equilateral triangle in half, the "half" is a 30-60 right triangle. The proportions are 1 (side), 2 (hypotenuse), squareroot of 3 (in this case, the height).
So the ratio of the height to a side is (square root of 3)x : 2x

Last edit: 2008-04-19 06:29:22

ieatkids5 United States. April 19 2008 06:31. Posts 4381

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last problem
multiply the top and the bottom by [(square root of 14) + (square root of 2)]
this gets rid of any radicals in the denominator

ieatkids5 United States. April 19 2008 06:35. Posts 4381

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problem 3
= 4(7) + 25(2) - 10(squareroot of 14) - 10(squareroot of 14)
= 78 - 20(squareroot of 14)

ieatkids5 United States. April 19 2008 06:35. Posts 4381

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problem 2
yes

Krzycho Poland. April 19 2008 06:35. Posts 442

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if i knew english word for math i would help ya, but i dont

QuanticHawk United States. April 19 2008 06:54. Posts 21160

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thank you very much man, ima wrap this up in a few

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goldenkrnboi United States. April 19 2008 07:05. Posts 2983

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+ Show Spoiler [1st problem answer] +

2nd problem is correct

+ Show Spoiler [3rd problem answer] +

+ Show Spoiler [4th problem answer] +

i don't have time to put the explanation. sorry.

Last edit: 2008-04-19 09:53:22

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gwho United States. April 19 2008 09:07. Posts 632

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to rationalize #4, multiply the denominator by its conjugate ( root 14 + root 2). you do foil, and the middle term cancels out and you're left with 14 - 2.

but keep in mind, when you multiply it by the conjugate, you multiply both the numerator and the denominator by the conjugate,which is the same thing as multiplying the entire term by 1 - which is why it is the same thing, right?

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