In a triangle, ABC, AP, the bisector of , is perpendicular to BC at point P. The measures of BP and PC are x and 3y, respectively. The measures of AB and AC are 4x and (5y + 21), what is the value of (x + y)?
Show answer & explanation
Correct answer: C
Explanation
The correct answer is option 3 i.e. 12.
Here,
BP/PC = AB/AC
⇒ x/3y = 4x/(5y + 21)
⇒ 5y + 21 = 12y
⇒ 7y = 21
⇒ y = 3
Now, In △APB and △APC
AP = AP [common]
∠P = ∠P = 90°
∠BAP = ∠CAP
Thus, △APB ≅ △APC
⇒ x = 3y
⇒ x = 3 × 3 = 9
So,
⇒ x + y = 9 + 3 = 12