SOLUTION: TEN is a right triangle with Angle T a right angle and TO an altitude to the hypotenuse. If TO= 12, OE is 7 more than NO, find NO and OE.

Question 1072820: TEN is a right triangle with Angle T a right angle and TO an altitude to the hypotenuse. If TO= 12, OE is 7 more than NO, find NO and OE.
Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
We use the altitude on hypotenuse theorem
:
Triangles NOT and TOE are similar to triangle TEN and to each other
:
let h be the altitude to the hypotenuse
:
let x be the length of NO, then OE = x + 7
:
h^2 = x * (x + 7)
:
12^2 = x^2 +7x
:
x^2 +7x - 144 = 0
:
(x + 16) * (x - 9) = 0
:
x = -16 or 9
:
we reject the negative value solution
:
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NO = 9 and OE = 9 + 7 = 16
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