MHB Find Length of Side in Right Triangle w/ 45°, 90°, and 45° Angle

[Monoxdifly]

The triangle ABC is a right triangle with A as the right angle and BD is the bisector of angle B. If AB = 12 cm and BC = 15 cm, the length of AD is ...
A. 3 cm
B. 4 cm
C. 5 cm
D. 6 cm
It was a question for a 9th grader and the book hasn't covered trigonometry by name yet (As in, they don't know about the term sine, cosine, and tangent, but the books do explain the length ratio of triangle which has 45°-90°-45° angle or 30°-60°-90° angle. How to do it and explain it to them?

 

[skeeter]

Pythagoras $\implies AC = 9$

using the ...

Angle Bisector Theorem

$\dfrac{AD}{AB} = \dfrac{CD}{BC}$

$\dfrac{AD}{12} = \dfrac{9-AD}{15}$

solve for $AD$

 

[Monoxdifly]

Angle Bisector Theorem

$\dfrac{AD}{AB} = \dfrac{CD}{BC}$

Never knew that this theorem exists. Gotta learn how it was derived from now.