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10 May 2016, 19:06
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63% (01:44) correct
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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.
A. 12
B. 18
C. 24
D. 28
E. 40
* A solution will be posted in two days.
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없음.png [ 7.94 KiB | Viewed 4350 times ]
10 May 2016, 20:38
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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
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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Triangle-slope.jpg [ 995.88 KiB | Viewed 4229 times ]
10 May 2016, 21:19
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MathRevolution
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
