Question

24. Rajeev and Amit sits together at B. Their
work places are at A and C respectively
such that A, B and C form a triangle. BD is
the bisector of ZABC, meets AC at right
angle. Various distances are expressed in
terms of x and y as shown in the following
figure.
B В
(3y+1) km
(5x - 2) km
Ay+1) km D(x + 2) km C
They used bicycles instead of bikes to go to
their work places. Find the distance
between A and C.​

Answer 1

Given : BD is the bisector of ∠ABC meets AC at right angle

AD = x + 2

DC = 2x+1

To Find  :  the distance between A and C.​

Solution:

BD is the bisector of ∠ABC meets AC at right angle

=> D is the mid point of AC

=> AD = DC

=> x + 2 = 2x + 1

=> x = 1

AD = x + 2 = 1 + 2 = 3

DC = 2(1) + 1 = 3

AC = AD + DC

= 3 + 3

= 6

the distance between A and C is 6  

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