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In x-y plane, there is a right triangle ABC (∠B=90o). If the length o

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In x-y plane, there is a right triangle ABC (∠B=90o). If the length o  [#permalink]

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New post 10 May 2016, 18:06
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In x-y plane, there is a right triangle ABC (∠B=90o). If the length of AC is 50 and the slope of line segment AC is 4/3, what is the length of AB?
A. 12
B. 18
C. 24
D. 28
E. 40

* A solution will be posted in two days.

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In x-y plane, there is a right triangle ABC (∠B=90o). If the length o  [#permalink]

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New post 10 May 2016, 19:38
Making things easy, lets take B at origin (0,0) and the triangle in II quadrant (because the hypotenuse needs to have +ve slope).
This gives us the coordinates of A: (0,y) and B: (-x,0)
Slope = 4/3
\(\frac{y-0}{0-(-x)} = \frac{4}{3}\)
\(\frac{y}{x} = \frac{4}{3}\)
y and x are in the ratio 4:3
y=4k and x=3k

Now, recall one of the most popular Pythagorean triplets- 3,4,5
Here, we already have two sides in ratio 3:4, so the third should be of the form 5k
Since AC=50, we get k=10
Hence, the other two sides are 30 and 40 respectively,

And AB = 40

Option E
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Re: In x-y plane, there is a right triangle ABC (∠B=90o). If the length o  [#permalink]

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New post 10 May 2016, 20:19
1
MathRevolution wrote:
In x-y plane, there is a right triangle ABC (∠B=90o). If the length of AC is 50 and the slope of line segment AC is 4/3, what is the length of AB?
A. 12
B. 18
C. 24
D. 28
E. 40

* A solution will be posted in two days.


Hi,
AC is the hyp and is 50...
the slope = 4/3, meaning the vertical rise is 4, when horizontal move is 3..
so ratio of vertical/horizontal =\(\frac{AB}{BC} = \frac{4}{3}\)....
clearly the right triangle is of 3:4:5... Now 5 is 50 here, so AB , which is in ratio 4 will be 4*10 = 40
E
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Re: In x-y plane, there is a right triangle ABC (∠B=90o).  [#permalink]

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New post 13 May 2016, 03:57
According the Pythagoras theorem, we get a^2+b^2=c^2. Normally, many problems involve 3^2+4^2=5^2. Hence, we can apply the rule to this question and get 30^2+40^2=50^2. Hence, the answer is 40 and the correct answer choice is E.

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Re: In x-y plane, there is a right triangle ABC (∠B=90o).   [#permalink] 13 May 2016, 03:57
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