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?
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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
