Problem: In a right triangle with sides a and b, and hypotenuse c, the altitude drawn on the hypotenuse is x. Then
Answer Choices:
A. a⋅b=x2
B. a1+b1=x1
C. a2+b2=2x2
D. x21=a21+b21
E. x1=ab
Solution:
The segments of the hypotenuse are ca2 and cb2. Using similar triangles, ax=bb2/c,bx=aa2/c.
∴x2=ca2⋅cb2=a2+b2a2b2; and ∴x21=a21+b21.