Question

What is the length of z ?

Answer 1

Answer:

The length of z is $3\sqrt{3}$ unit

Step-by-step 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

$y=\sqrt{108}$

on simplify we get,  $y=6\sqrt{3}$ unit

Therefore, the length of BC is $6\sqrt{3}$ 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 = $6\sqrt{3}$ unit and DC = 9 units we have,

$z^2+9^2=(6\sqrt{3})^2$ or

$z^2+81=108$ or

Simplify:

$z^2=27$  or

$z=\sqrt{27} = 3 \sqrt{3}$

Therefore, the value of length z is $3\sqrt{3}$ unit

Answer 2

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