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?
Following are the vertexes of a triangle, (0,0), (0,a) and..
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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.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?
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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