SOLUTION: Will you please help me find the altitude on an acute scalene triangle? The problem is I have been given only the AREA(90 square feet) and the hypotenuse(18 feet). Am I correct i

Algebra ->  Triangles -> SOLUTION: Will you please help me find the altitude on an acute scalene triangle? The problem is I have been given only the AREA(90 square feet) and the hypotenuse(18 feet). Am I correct i      Log On


   

Question 597319: Will you please help me find the altitude on an acute scalene triangle? The problem is I have been given only the AREA(90 square feet) and the hypotenuse(18 feet). Am I correct in making the assumption the missing part is the base and without its amount of feet an impossible equation to solve with a formula? Thank you for your time and expertise.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
The problem is I have been given only the AREA(90 square feet) and the hypotenuse(18 feet).
:
The fact that they give you the hypotenuse, means it is a right triangle, so we can call one side the altitude (a) and the other side the base (b)
:
We know is the two sides are different because it is a scalene triangle, using pythag
sqrt%28a%5E2%2Bb%5E2%29 = 18
and the area
1%2F2b*a = 90
mult both sides by 2
a * b = 180
b = 180%2Fa
:
replace b
sqrt%28a%5E2+%2B+%28180%2Fa%29%5E2%29 = 18
square both sides
a^2 + (180/a)^2 = 324
a^2 + (180/a)^2 - 324 = 0
:
Plot this equation
+graph%28+300%2C+200%2C+-20%2C+20%2C+-100%2C+500%2C+x%5E2%2B%28180%2Fx%29%5E2-324%29+
I don't think there is a solution, no x (a) intercept