AAPL wrote:Following are the vertexes of a triangle, (0,0), (0,a) and (a,b). What is the area of triangle?
1) Hypotenuse of triangle is 10.
2) a and b are positive integers.
The OA is C.
How can I do for solve this DS question? I don't understand why that is the correct answer? Please, can any expert help me to solve it?
Plotting the three vertices on the Cartesian plane, we find that one of the vertices (0, 0) lies at the center, the second one (0, a) lies on the X-axis, and the third one (b, 0) lies on the Y-axis. Thus, this makes a rightangled triangle with base and height equal to a and b. Thus, the area of the triangle = a*b/2.
Question rephrased: What's the value of ab?
1) The hypotenuse of the triangle is 10.
=> a^2 + b^2 = 10^2 = 100. We cannot get the unique value of ab. There can be many possible values of a and b, leading to many possible values of ab. Insufficient,
2) a and b are positive integers.
Certainly insufficient.
(1) and (2) combined:
This calls for recalling Pythagorean triplets.
One of the Pythagorean triplets 6, 8, and 10, where 10 is hypotenuse and 6 & 8 are base and height, works here. If you try to find out other possible values of base and height that are integers, it is not possible.
Say height = 9, thus base = √(10^2 - 9^2) = √(100 - 81) = √19 = not an integer. Not possible!
Say height = 10, thus base = √(10^2 - 10^2) = 0; not possible since then the traingle will not exist.
Thus, a = 6 and b = 8 => ab = 48. Sufficient.
The correct answer:
C
Hope this helps!
-Jay
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