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

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
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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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10 May 2016, 18:06
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25% (medium)

Question Stats:

78% (02:01) correct 22% (01:54) wrong based on 39 sessions

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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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.png [ 7.94 KiB | Viewed 965 times ]

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MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
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"Only $79 for 1 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" Manager Status: One Last Shot !!! Joined: 04 May 2014 Posts: 225 Location: India Concentration: Marketing, Social Entrepreneurship GMAT 1: 630 Q44 V32 GMAT 2: 680 Q47 V35 In x-y plane, there is a right triangle ABC (∠B=90o). If the length o [#permalink] ### Show Tags 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 Attachments Triangle-slope.jpg [ 995.88 KiB | Viewed 927 times ] Math Expert Joined: 02 Aug 2009 Posts: 8297 Re: In x-y plane, there is a right triangle ABC (∠B=90o). If the length o [#permalink] ### Show Tags 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 _________________ Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 8722 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: In x-y plane, there is a right triangle ABC (∠B=90o). [#permalink] ### Show Tags 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. Attachments 2.png [ 8.45 KiB | Viewed 854 times ] _________________ MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only$79 for 1 month Online Course"
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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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