Question

Find the value of z

Answer 1

C. 50

Explanation:

We are given ΔABC with an altitude BD as shown in the figure.

As it is known that,

'When an altitude is drawn from a right angle of a triangle, then all the three triangles are congruent.'

So, we get that ΔABC ≅ ΔABD ≅ CBD.

Since, the triangles are congruent, their corresponding sides and angles will be congruent.

Moreover, the ratio of the sides will be equal.

So, we get from ΔABC ≅ ΔABD,

`(AD)/(AB)=(AB)/(AC)`

i.e.
`AD=(AB* AB)/(AC)`

i.e.
`18=(30* 30)/(z)`

i.e.
`18=(900)/(z)`

i.e.
`z=(900)/(18)`

i.e. z = 50.

Hence, the value of z is 50.