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23 Apr 2011, 13:16
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If the hypotenuse of a right angle triangle = 5, are the legs of that right angle triangle always 3 and 4?
I ask because I came across a data sufficiency question that stated the diagonal of a rectangle was 5 ie. the hypotenuse of the triangle = 5. I assumed this meant the Length and Width (the legs) were 3 and 4. However, it stated that it could be 5^2 = square root 15^2 + square root 10^2 or 5^2= square root 5^2 + square root 20^2. What am I missing about the 3-4-5 right angle triangle formula?
I ask because I came across a data sufficiency question that stated the diagonal of a rectangle was 5 ie. the hypotenuse of the triangle = 5. I assumed this meant the Length and Width (the legs) were 3 and 4. However, it stated that it could be 5^2 = square root 15^2 + square root 10^2 or 5^2= square root 5^2 + square root 20^2. What am I missing about the 3-4-5 right angle triangle formula?
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23 Apr 2011, 13:35
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Have the measures of the two sides been mentioned specifically as being integers? If yes, I would possibly have thought in the same manner that you did.
Apparently, the squares of a lot of positive number pairs can add up to 25 (=5^2). Any such pair would be ideal to describe the other two sides. For example, you could consider sqrt(17), and sqrt(8) as one of the possible pairs. Another one could be 5/2 and 5*sqrt(3)/2. In fact, you can think of an infinite number of such pairs. But essentially, these will all be members of the real numbers set, (a super set of Integers) to be precise.
Regards
Rahul
Apparently, the squares of a lot of positive number pairs can add up to 25 (=5^2). Any such pair would be ideal to describe the other two sides. For example, you could consider sqrt(17), and sqrt(8) as one of the possible pairs. Another one could be 5/2 and 5*sqrt(3)/2. In fact, you can think of an infinite number of such pairs. But essentially, these will all be members of the real numbers set, (a super set of Integers) to be precise.
Regards
Rahul
23 Apr 2011, 13:38
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Ah, of course, I guess the 3-4-5 rule applies if and only if x, y, and z are integers. Bah, that restriction (or lack thereof) always kills me in data sufficiency. Thanks.
