In , and the two legs are equal, . The perpendicular from meets at…

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

Problem

\triangle ABC

\angle C = 90^{\circ}

and the two legs are equal,

AC = BC = 10\,\text{cm}

. The perpendicular from

C

meets

AB

D

. (a) Prove that

\triangle ACD \cong \triangle BCD

. (b) Find the length of

CD

. (c) Determine the lengths of

AD

and

BD

. (d) Calculate the area of

\triangle ABC

. (Leave

\sqrt{}

terms if necessary.)