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The vertices of a triangle have coordinates

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The vertices of a triangle have coordinates

by gmatdriller » Tue Sep 28, 2010 10:01 pm
The vertices of a triangle have coordinates (x,1), (5,1) and (5,y) where x<5
and y>1.

What is the area of the triangle?

1. x= y
2. Angle at the vertex (x,1) = angle at the vertex (5,y)

I chose B because since two of the angles are equal, it is enough information
to signify an isosceles triangle; however, I got it wrong.

OA is C
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by Rahul@gurome » Tue Sep 28, 2010 10:34 pm
If you draw the figure on coordinate plane, you will see that above will be a right angled triangle with 90 degree at vertex (5,1).
The length of perpendicular sides are (y-1) and (5-x).

So area will be ½ * (y-1) * (5-x). To compute this we need both the values of x and y.

Consider first statement (1) alone.
x=y does not give us their individual values.
So (1) alone is not sufficient.
Next consider (2) alone.
Angle at the vertex (x,1) = angle at the vertex (5,y).
This means it is an isosceles right angled triangle.
Or it means the perpendicular sides are same.
Or (y-1) = (5-x).
But again we are not getting the values of x and y individually.
So (2) alone is not sufficient.

Next consider both (1) and (2) combined.
It means x = y and (y-1) = (5-x).
This means y-1 = 5-y.
Or 2y = 6 or y = 3.
So (y-1) = 2.
Or area is ½ * 2 * 2 = 2.

The correct answer is hence (C).
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by gmatdriller » Fri Oct 01, 2010 9:20 am
oh, condition (2) specifies that the right-angled triangle could have infinitely
many values. e.g Height =2, base=2, area=2; also, height=3, base=3 ==>
area=4.5 etc, etc. So, (2) is INSUFFICIENT.

combining yields a boundary condition that y=x=3, so, area = 4.5
Appreciate.
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by GMATMadeEasy » Fri Oct 01, 2010 12:28 pm
Good question. Is it GMATPrep question ?
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