In ( ABC ), ( B = 90^ )

MATHEMATICS · Multi-part · CBSE · Mathematics · Triangles · Triangles

Problem

\triangle ABC

\angle B = 90^\circ

. The perpendicular from

B

to the hypotenuse

AC

meets

AC

D

. Given that

AB = 6\,\text{cm}

and

BC = 8\,\text{cm}

, answer the following: (i) Prove that

\triangle ADB \sim \triangle ABC

. (ii) Using the result of part (i), show that

AD \cdot AC = AB^2

. (iii) Hence find the length of

AD

. (iv) Calculate the length of the altitude

BD