Question

Find the value of each variable (geometry)

Answer 1

The values of variables are

y =
`√(13)`

x = DA -3

z = 2 + DA -3

As per given information,

AD = y

BC = x

CD = 2

CA = 3

BD = 2 + x = z

To find the y use Pythagoras' theorem

`AC^2 + CD^2 = DA^2`

`3^2 + 2^2 = DA^2`

9 + 4
`= DA^2`

13 =
`DA^2`

DA =
`√(13)`

To find the x use Pythagoras' theorem

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

`3^2 + x^2 = DA^2`

`x^2 = DA^2 -3^2`

Cancelling square of both sides

`x = DA -3`

The value of z

= 2 + x

z = 2 + DA -3

Answer 2

2/3=3/x
2x=9
x=4.5
z=2+4.5
z=6.5
2/y=y/6.5
y^2=13
y= 3.61