Question

When an altitude is drawn to the hypotenuse of a right triangle, the lengths of the segments of the hypotenuse are 16 and 25. What is the length of the altitude?

Answer 1

20
25
41
50
@jim_thompson5910

Answer 2

If you draw the picture, you'll have 3 right triangles.


One with legs x and y, with hypotenuse 41


One with legs A and 25, with hypotenuse y


and another one with legs 16 and A, with hypotenuse x


So use the pythagorean theorem to get the three equations

x^2+y^2 = 41^2
A^2+25^2 = y^2
16^2+A^2 = x^2


Then solve for A


16^2+A^2+y^2 = 41^2
16^2+A^2+A^2+25^2 = 1681
256+2A^2+625 = 1681
2A^2 = 1681
2A^2 = 800
A^2 = 400
A = 20


So the answer is choice A