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 ?

Question

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 ? (A) 74 (B) 84 (C) 91 (D) 105

Tardigrade Admin · Accepted Answer

(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.

Q. In the following figure, $∠ A BC = 9 0^{\circ}, A D = 15$ and $D C = 20$ . If $B D$ is the bisector of $∠ A BC$ , what is the perimeter of the triangle $A BC$ ?

74

84

91

105

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

Q. In the following figure, ∠ABC=90∘,AD=15 and DC=20. If BD is the bisector of ∠ABC, what is the perimeter of the triangle ABC ?

74

84

91

105

(i) Apply 'angle bisector theorem'. (ii) AB:BC=AD:DC. (iii) Apply Pythagoras theorem, and find AB and BC.

Q. In the following figure, $∠ A BC = 9 0^{\circ}, A D = 15$ and $D C = 20$ . If $B D$ is the bisector of $∠ A BC$ , what is the perimeter of the triangle $A BC$ ?

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