Question

In Δ ABC, angle BAC = 90°, AD┴BC BD = 4cm, CD = 5cm find x and y

Answer 1

Step-by-step explanation:

let AB = x, BD = y, and BC = z

from triangle ABC

x2 + z2 =(4+5)2=81 --------(1)

from triangle ADB

x2= y2+16 ------------(2)

from triangle BDC

z2= y2 + 25 ----------(3)

substituting (2) and (3) in (1)

(y2+16)+(y2+25)=81

y2 =20------------(4)

y=2 root 5

substituting (4) in 2

x2= 20+ 16

x=6

thus BD = 2 root 5

AB=6