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. aâ‹…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​.