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  4. In the following figure, angle A B C=90°, A D=15 and D C=20. If B D is the bisector of angle A B C, what is the perimeter of the triangle A B C ?

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Q. In the following figure, $\angle A B C=90^{\circ}, A D=15$ and $D C=20$. If $B D$ is the bisector of $\angle A B C$, what is the perimeter of the triangle $A B C$ ?Mathematics Question Image

Geometry

Solution:

(i) Apply 'angle bisector theorem'.
(ii) $A B: B C=A D: D C$.
(iii) Apply Pythagoras theorem, and find $A B$ and $B C$.