Question 15

In the following diagram, 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

Solution

In the question, it is given that area of triangle ABC is 2 times the area of triangle ABD.

$$\frac{1}{2}x\left(y+z\right)=2\left(\frac{1}{2}xy\right)$$

y + z = 2y

y = z

Triangles ABC and ABD are right-angled triangles.

$$W^2=x^2+4y^2$$

$$W^2=x^2+y^2+3y^2$$

$$AD^2=x^2+y^2$$

$$AD^2=W^2-3y^2$$

$$AD=\sqrt{\ W^2-3y^2}$$

The answer is option C.

Video Solution

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