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?

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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
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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)?
10?
Perfect. Now what's the formula for area of a triangle?

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A = 1/2 base times height?
Right on. What's the distance between (7, 2) and (7, b) in terms of b?
And assuming b is positive.
I'm not sure, that's the part I don't get D: I don't know how to solve it.
Well, there's two ways to look at it. The easy way, or the hard way. The hard way uses the distance formula. \[\sqrt{(b-2)^2+(7-7)^2} =\sqrt{(b-2)^2}=b-2\]
yeah, that's what I tried to do.
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.
mhmm, then?
One last thing. What's the base and the height of the triangle?
well, the base would be 10 since we figured that out and aren't we trying to find the height right now?
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?
It's perpendicular?
Right.
|dw:1338696349644:dw|Can you tell me what the area of this triangle is?
5b - 10? ._. idk...
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?
well, they gave it to us that the area is 45.
can i suggest another method?
Go ahead.
ohmigosh ._. what is that? ._.
sorry, but I don't think I learned that LOL
Back to the first way then.
LOL sorry, dpalnc :(
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?
i don't know why but I got 9.4....
I don't know why either :P You should get \[A=45=\frac{1}{2}\cdot10\cdot(b-2)=5\cdot(b-2)\]
Can you solve the equation \[45=5(b-2)\]for \(b\)?
yeahh so then that would become: 45 = 5b -10.. OH. OKAY HOLD ON. I MADE A MISTAKE LOL
B = 11 !!!
Perfect. Great job.
OHMIGOSH THANK YOU SO MUCH :D YOU HELPED ME SO MUCH THANK YOU THANK YOU THANK YOU THANK YOU THANK YOU :D
You're welcome :)
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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