In an isosceles triangle ABC, AB= AC = 2a and BC-a. Find the length of altitude AD.
2a
B
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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
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