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### TANCET 2008 - Past year question paper: Right Triangles, hypotenuse, geometry : Ascent Education TANCET MBA Classes

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# TANCET 2008 Quant Question 9 : Geometry - Right Triangles

## Question

If the shaded area is one half the area of triangle ABC and angle ABC is right angle, then the length of line segment AD is
1. c
Correct Answer: . Choice (4)

The area of triangle ABD is half the area of triangle ABC.
Both triangles have the same base AB.
So, the altitude BD of triangle ABD is half the altitude BC of triangle ABC.

So, z = y.
Now, AD is the hypotenuse of the triangle ABD.
So, AD = .... exp (1)
In triangle ABC, AC2 = w2 = x2 + (y + z)2
But y = z, so we can rewrite the expression as w2 = x2 + (y + y)2
Or w2 = x2 + 4y2
Or x2 = w2 - 4y2

Substituting this value of x2 in exp (1), we get

Level of difficulty : Moderate

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