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

Composing answer soon...

PartialMathematician  Nov 21, 2018



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



cool cool laugh

CPhill  Nov 21, 2018

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