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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?

 Nov 20, 2018
 #1
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Composing answer soon...

 Nov 21, 2018
 #2
avatar+105238 
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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

 

 

cool cool laugh

 Nov 21, 2018

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