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 2 years ago
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?
 2 years ago
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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KingGeorge
 2 years ago
Best ResponseYou've already chosen the best response.1If you were to graph this, you could probably see what to do. dw:1338695720852:dwYou 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)?

KingGeorge
 2 years ago
Best ResponseYou've already chosen the best response.1Perfect. Now what's the formula for area of a triangle?

xRAWRRx3
 2 years ago
Best ResponseYou've already chosen the best response.1A = 1/2 base times height?

KingGeorge
 2 years ago
Best ResponseYou've already chosen the best response.1Right on. What's the distance between (7, 2) and (7, b) in terms of b?

KingGeorge
 2 years ago
Best ResponseYou've already chosen the best response.1And assuming b is positive.

xRAWRRx3
 2 years ago
Best ResponseYou've already chosen the best response.1I'm not sure, that's the part I don't get D: I don't know how to solve it.

KingGeorge
 2 years ago
Best ResponseYou've already chosen the best response.1Well, there's two ways to look at it. The easy way, or the hard way. The hard way uses the distance formula. \[\sqrt{(b2)^2+(77)^2} =\sqrt{(b2)^2}=b2\]

xRAWRRx3
 2 years ago
Best ResponseYou've already chosen the best response.1yeah, that's what I tried to do.

KingGeorge
 2 years ago
Best ResponseYou've already chosen the best response.1The 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 \(b2\). Once again, assuming b is greater than 2.

KingGeorge
 2 years ago
Best ResponseYou've already chosen the best response.1One last thing. What's the base and the height of the triangle?

xRAWRRx3
 2 years ago
Best ResponseYou've already chosen the best response.1well, the base would be 10 since we figured that out and aren't we trying to find the height right now?

KingGeorge
 2 years ago
Best ResponseYou've already chosen the best response.1We know that the distance from (7, 2) to (7, b) is b2, and it's a vertical line. What does that tell you about the height of the triangle?

KingGeorge
 2 years ago
Best ResponseYou've already chosen the best response.1dw:1338696349644:dwCan you tell me what the area of this triangle is?

KingGeorge
 2 years ago
Best ResponseYou've already chosen the best response.1In this triangle, the base is of length 10, and the height is b2. Using the formula for the area of a triangle, what do you get as the area?

xRAWRRx3
 2 years ago
Best ResponseYou've already chosen the best response.1well, they gave it to us that the area is 45.

dpaInc
 2 years ago
Best ResponseYou've already chosen the best response.0can i suggest another method?

xRAWRRx3
 2 years ago
Best ResponseYou've already chosen the best response.1ohmigosh ._. what is that? ._.

xRAWRRx3
 2 years ago
Best ResponseYou've already chosen the best response.1sorry, but I don't think I learned that LOL

KingGeorge
 2 years ago
Best ResponseYou've already chosen the best response.1Back to the first way then.

KingGeorge
 2 years ago
Best ResponseYou've already chosen the best response.1You're given that the area is 45, the base is of length 10, and the height is b2. Now use your formula of \[A=\frac{1}{2}bh\]with \(b=10\) and \(h=b2\) (those are different \(b\)'s). What do you get?

xRAWRRx3
 2 years ago
Best ResponseYou've already chosen the best response.1i don't know why but I got 9.4....

KingGeorge
 2 years ago
Best ResponseYou've already chosen the best response.1I don't know why either :P You should get \[A=45=\frac{1}{2}\cdot10\cdot(b2)=5\cdot(b2)\]

KingGeorge
 2 years ago
Best ResponseYou've already chosen the best response.1Can you solve the equation \[45=5(b2)\]for \(b\)?

xRAWRRx3
 2 years ago
Best ResponseYou've already chosen the best response.1yeahh so then that would become: 45 = 5b 10.. OH. OKAY HOLD ON. I MADE A MISTAKE LOL

xRAWRRx3
 2 years ago
Best ResponseYou've already chosen the best response.1OHMIGOSH THANK YOU SO MUCH :D YOU HELPED ME SO MUCH THANK YOU THANK YOU THANK YOU THANK YOU THANK YOU :D

dpaInc
 2 years ago
Best ResponseYou've already chosen the best response.0here 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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