The following seems an easy question, to get the area of the rectangluar triangle with the slope equals to 10 and the height equals to 6.
If your answer is 30 (10×6/2), then you are falling into the trap: Such triangle doesn’t exist at all!
It does not exist!
If we label the triangle with the following,
What we can get are:
If we add these two equations:
After simplification, we have:
Thus,
because .
If, , , we can plot the graph,
The maximum value for function y is 25, which means that the maximum value of c is
Such triangle does not exist (the height is 6, which exceeds the maximum length)!
Typical Microsoft. If something is wrong then it is by design…and you are stuck with it.
–EOF (The Ultimate Computing & Technology Blog) —
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Official solution is wrong. Formalization of the problem is:
Find a real number x such that sentence
“If ABC is triangle with right angle in A, |BC|=10 and height from A is 6, then the area of the triangle is x”
is true.
Because no such triangle and false implies any proposition, any real number x is solution.
You should have gotten the clue of the impossibility when you read that this was a “rectanGLUAR” triangle. Is there such a thing? It was even written twice!
You can also draw the median which starts from the right angle, which has length 5, and take into account that the shortest line from the tip of the right angle to the hypotenuse is the height, which would imply that 6<5