Question

Find the value of z

Answer 1

Answer:

C. 50

Step-by-step 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,

$\frac{AD}{AB}=\frac{AB}{AC}$

i.e. $AD=\frac{AB\times AB}{AC}$

i.e. $18=\frac{30\times 30}{z}$

i.e. $18=\frac{900}{z}$

i.e. $z=\frac{900}{18}$

i.e. z = 50.

Hence, the value of z is 50.