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QuanticHawk
United States32097 Posts
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. ![[image loading]](http://www.webassign.net/mckialg/7-4-047.gif) multiply ![[image loading]](http://www.webassign.net/www22/symImages/a/3/44f2873309fe3e3148e2bb27953269.gif) this is 2 (SRT) 14 - 14, right? ![[image loading]](http://www.webassign.net/www22/symImages/b/b/73d4073c57124c1008daf6450413b3.gif) multiply Rationalize the denominator in the following. ![[image loading]](http://www.webassign.net/www22/symImages/a/4/ff3795db77b8156426608f8d30ecbd.gif) thanks!!   | ||
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ieatkids5
United States4628 Posts
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 | ||
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ieatkids5
United States4628 Posts
multiply the top and the bottom by [(square root of 14) + (square root of 2)] this gets rid of any radicals in the denominator | ||
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ieatkids5
United States4628 Posts
= 4(7) + 25(2) - 10(squareroot of 14) - 10(squareroot of 14) = 78 - 20(squareroot of 14) | ||
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ieatkids5
United States4628 Posts
yes | ||
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Krzycho
Poland442 Posts
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QuanticHawk
United States32097 Posts
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Deleted User 30223
3104 Posts
(radical 3) : 2 + Show Spoiler [explanation] + altitudes of an equilateral triangle form a 30-60-90 triangle, so the side opposite of the 60 angle (the untouched angle) is equal to (radical 3)/2 of the hypotenuse. therefore, the ratio is (radical 3)/2 2nd problem is correct + Show Spoiler [3rd problem answer] + 78 - 20(radical 14) + Show Spoiler [explanation] + 2 * (radical 7) squared = 28+ Show Spoiler + 2 * (radical 7) squared becomes 2 squared plus (radical 7) squared, so it becomes 4 * 7, which is 28 when a binomial(an expression with 2 different terms) is squared, you can follow the equation a squared (where a is the first term) + 2ab (where b is the second term) + b squared or a squared - 2ab + b squared, depending on the symbols. since you're subtracting, you follow a squared - 2ab + b squared. + Show Spoiler [4th problem answer] + (radical 7) - 1 / 6 i don't have time to put the explanation. sorry. | ||
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gwho
United States632 Posts
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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