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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.
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