anonymous
  • anonymous
Please help :( A right triangle with area 45 has vertices at (-3, 2), (7, 2), and (7, b), where b > 0. What is the value of b?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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KingGeorge
  • KingGeorge
If you were to graph this, you could probably see what to do. |dw:1338695720852:dw|You want a point on that line so that the area is 45. Can you tell me what the distance is between (-3, 2) and (7, 2)?
anonymous
  • anonymous
10?
KingGeorge
  • KingGeorge
Perfect. Now what's the formula for area of a triangle?

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anonymous
  • anonymous
A = 1/2 base times height?
KingGeorge
  • KingGeorge
Right on. What's the distance between (7, 2) and (7, b) in terms of b?
KingGeorge
  • KingGeorge
And assuming b is positive.
anonymous
  • anonymous
I'm not sure, that's the part I don't get D: I don't know how to solve it.
KingGeorge
  • KingGeorge
Well, there's two ways to look at it. The easy way, or the hard way. The hard way uses the distance formula. \[\sqrt{(b-2)^2+(7-7)^2} =\sqrt{(b-2)^2}=b-2\]
anonymous
  • anonymous
yeah, that's what I tried to do.
KingGeorge
  • KingGeorge
The easy way is to look at the graph. It's a straight vertical line from (7, 2) to (7, b), so the distance is just \(b-2\). Once again, assuming b is greater than 2.
anonymous
  • anonymous
mhmm, then?
KingGeorge
  • KingGeorge
One last thing. What's the base and the height of the triangle?
anonymous
  • anonymous
well, the base would be 10 since we figured that out and aren't we trying to find the height right now?
KingGeorge
  • KingGeorge
We know that the distance from (7, 2) to (7, b) is b-2, and it's a vertical line. What does that tell you about the height of the triangle?
anonymous
  • anonymous
It's perpendicular?
KingGeorge
  • KingGeorge
Right.
KingGeorge
  • KingGeorge
|dw:1338696349644:dw|Can you tell me what the area of this triangle is?
anonymous
  • anonymous
5b - 10? ._. idk...
KingGeorge
  • KingGeorge
In this triangle, the base is of length 10, and the height is b-2. Using the formula for the area of a triangle, what do you get as the area?
anonymous
  • anonymous
well, they gave it to us that the area is 45.
anonymous
  • anonymous
can i suggest another method?
KingGeorge
  • KingGeorge
Go ahead.
anonymous
  • anonymous
ohmigosh ._. what is that? ._.
anonymous
  • anonymous
sorry, but I don't think I learned that LOL
KingGeorge
  • KingGeorge
Back to the first way then.
anonymous
  • anonymous
LOL sorry, dpalnc :(
KingGeorge
  • KingGeorge
You're given that the area is 45, the base is of length 10, and the height is b-2. Now use your formula of \[A=\frac{1}{2}bh\]with \(b=10\) and \(h=b-2\) (those are different \(b\)'s). What do you get?
anonymous
  • anonymous
i don't know why but I got 9.4....
KingGeorge
  • KingGeorge
I don't know why either :P You should get \[A=45=\frac{1}{2}\cdot10\cdot(b-2)=5\cdot(b-2)\]
KingGeorge
  • KingGeorge
Can you solve the equation \[45=5(b-2)\]for \(b\)?
anonymous
  • anonymous
yeahh so then that would become: 45 = 5b -10.. OH. OKAY HOLD ON. I MADE A MISTAKE LOL
anonymous
  • anonymous
B = 11 !!!
KingGeorge
  • KingGeorge
Perfect. Great job.
anonymous
  • anonymous
OHMIGOSH THANK YOU SO MUCH :D YOU HELPED ME SO MUCH THANK YOU THANK YOU THANK YOU THANK YOU THANK YOU :D
KingGeorge
  • KingGeorge
You're welcome :)
anonymous
  • anonymous
here is the thing that i was suggesting to find the area of a triangle using matrices: http://www.youtube.com/watch?v=a5C_I5Fywfo

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