In isosceles right triangle ABC, point D is on hypotenuse BC such that AD is an altitude of ABC and DC=5. What is the area of triangle ABC?

Guest Nov 20, 2018

#2**+1 **

An altitude drawn to the hypotenuse of an isosceles right triangle always bisects the hypotenuse

So BD = CD

And AD forms a geometric mean of BD and CD

So....we have this relationship

BD / AD = AD / CD but BD = CD ...so...

BD / 5 = 5 / BD

BD^2 = 25

BD = 5

But BD is 1/2 of base BC

And AD is an altitude of ABC drawn to this base

So....the area of ABC = (1/2)BC * AD = 5 * 5 = 25 units^2

CPhill Nov 21, 2018