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The area of a right triangle is 6$\sqrt{2}$ square centimeters and the length of one leg is $\sqrt{12}$ cenimeters.What is the length of the other leg?What is the length of the hypotenuse?

a) 2$\sqrt{6} \mathrm{cm}$b) 6 $\mathrm{cm}$

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Chapter 3

REAL NUMBERS AND RADICALS

Section 6

Dividing Radicals

Whole which of Numbers

Fractions and Mixed Numbers

Decimals

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The length of one leg of a…

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Use the Pythagorean Theore…

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the hypotenuse of a right …

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The length of the hypotenu…

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The length of the shorter …

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I always like to draw a picture for a problem like this. So I'm giving one side of my right triangle, and I'm trying to find the height. So if I know the area, my formula is areas 1/2 base times height. I would substitute the area in for a I'm giving one side. So I plugged it in for B and I'm trying to find the height by multiply both sides by two. I can reduce here and this on the left side, I'm left with 12 times the square to two on the right side. I'm left with the square to 12 times H divide both sides by this word of 12 leaves me with on the left side I can reduce the squared of two and this word of 12 to make my number smaller. So that would wind up giving me that slide up here That would give me 12. Divided by this word of six equals h. I can't leave a radical in the denominator. Some going to rationalize that the nominator by multiplying the top and bottom by the squared of six and I multiply by one. It doesn't change the value which has changed what it looks like. So I have 12 times a squared of six, divided by the square root of 36 which is just six, and I would equal my height. Finally, I can reduce the six goes into 12 twice, and I get two times. The square of six equals my height. Finally, I'm asked to find the length of the high pod news. I'll call that. See if my H is too times this word of six. I can use the Pythagorean theorem and I can say two times a squared of six squared. Plus, the square root of 12 squared equals C squared so that the factory theorem is a squared plus B squared equals C squared, where a and B are the two legs. If I square the squared of 12 that's easy. That just gives me 12 when I square two times this word of six to swear it is four. This word of six times it's where two sixes, the sweat of 36 which is just six, and I would equal C Square, so four times six gives me 24 plus 12 gives me C squared 36 seat will c squared. Take the square root of both sides and I know it can't be a negative because it's a side of a triangle, so I get six equals.

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