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. 
2. c
3. 
4. 
5. 

Correct Answer: . Choice (4)

Explanatory Answers

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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