Question

In the ∆ABC given below, BD bisects ∠B and is perpendicular to AC. If the lengths of the sides of the triangle are expressed in terms of x and y as shown, find the values of x and y.

Answer 1

Explanation:

Please look at the attachment for solution

Answer 2

Explanation:

In figure

TriangleADB AND TRIANGLE CDB

BD BISECTS ANGLE B

angle ABD =DBC

SIDE BD =DB............. COMMON SIDE

ANGLE ADB=BDC............. EACH 90°

ADB =CDB.........ASA TEST OF CONGUENCY

AB=BC........... C.S.C.T

2x=3y+8

2x-3y=8...............1

AD=DC

x=2y

x-2y=0...............2

Multiplying equation 2 by 2

2x-4y=0...............3

Subtracting equation 1 from 3

+2x-3y=+8

+2x-4y=+0

- +. -

y=8

Substitute inequation 1 2 or 3 u will get the answer