Question

What is the length of z ?

Answer 1

it's close to six and it's shorter so 5?

Answer 2

The length of z is
`3√(3)` unit

Explanation:

First Label the diagram as shown in the attachment:

In right
`\triangle ABC`;

first find the value of y:

Use Pythagoras theorem states that in a right angled triangle, the square of the hypotenuse is equal to the sum of the squares on the other two sides.

In
`\triangle ABC`

length of AB =6 unit , length of BC =y unit and the length of AC = 3+9 =12 unit

Now, using Pythagoras theorem to get the value of y;

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

`6^2+y^2=12^2` or

`36+y^2=144` or

`y^2=144-36`=108 or

`y=√(108)`

on simplify we get,
`y=6√(3)` unit

Therefore, the length of BC is
`6√(3)` unit.

now, in
`\triangle BDC`

using Pythagoras theorem to find the value of z;

`BD^2+CD^2=BC^2`

Putting the values of BD = z units , BC =
`6√(3)` unit and DC = 9 units we have,

`z^2+9^2=(6√(3))^2` or

`z^2+81=108` or

Simplify:

`z^2=27` or

`z=√(27) = 3 √(3)`

Therefore, the value of length z is
`3√(3)` unit