Question

What is the value of m in the figure below? In this diagram, ABD ~ BCD.

Answer 1

Answer : The value of m is,
`√(136)`

Step-by-step explanation :

Using Pythagoras theorem in ΔABC :

`(Hypotenuse)^2=(Perpendicular)^2+(Base)^2`

`(AC)^2=(AB)^2+(BC)^2`

`(9+8)^2=(AB)^2+(m)^2`

`(17)^2=(AB)^2+(m)^2` .............(1)

Using Pythagoras theorem in ΔBDC :

`(Hypotenuse)^2=(Perpendicular)^2+(Base)^2`

`(BC)^2=(BD)^2+(DC)^2`

`(m)^2=(BD)^2+(8)^2` ............(2)

Using Pythagoras theorem in ΔBDA :

`(Hypotenuse)^2=(Perpendicular)^2+(Base)^2`

`(AB)^2=(BD)^2+(DA)^2`

`(AB)^2=(BD)^2+(9)^2`

`(AB)^2-(9)^2=(BD)^2` ..........(3)

Substituting equation 3 and 2, we get:

`(m)^2=(BD)^2+(8)^2`

`(m)^2=(AB)^2-(9)^2+(8)^2`

`(m)^2=(AB)^2-81+64`

`(m)^2+17=(AB)^2` ...........(4)

Now put equation 4 in 1, we get:

`(17)^2=(AB)^2+(m)^2`

`(17)^2=(m)^2+17+(m)^2`

`(17)^2-17=2m^2`

`289-17=2m^2`

`272=2m^2`

`m=\sqrt{(272)/(2)}`

`m=√(136)`

Thus, the value of m is,
`√(136)`