Question

(ii) ABC is an isosceles triangle with
AB = AC = 2a and BC = a. If ADIBC,
find the length of AD.​

Answer 1

Answer:

In an isosceles ΔABC in which AB=AC=2a units, BC=a units

AD is the altitude. Therefore, D is the midpoint of BC

⇒BD=

2

a

We have two right triangles: ΔADB and ΔADC

By Pythagoras theorem,

AB

2

=BD

2

+AD

2

(2a)

2

=(a/2)

2

+AD

2

(2a)

2

=

4

a

2

+AD

2

AD

2

=

4

16a

2

−a

2

=

4

15a

2

AD=

2

a

15