Question

if angle C =90°,then area of triangle ABC is​

Answer 1

Answer:

In a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

In △ACD

AD2=AC2+CD2   .....(1)

In △ACB

AB2−AC2=BC2    .....(2)

As CD=DB=2BC   ...... (3)

Substituting (3) in (1)

AD2=AC2+4BC2 

4AD2−4AC2=BC2    ....... (4)

Subtracting (2) from (4)

4AD2−4AC2−(AB2−AC2)=BC2−BC2 

4AD2−4AC2−AB2+AC2=0 

4AD2−3AC2=AB2 

Hence proved.