In the diagram below, triangle MTH is a right triangle and segment HA is an altitude.
MA = 9 cm and AT = 15 cm.

Determine the lengths of segments HA, HM, and HT.





Solution to the Problem:




Let x = length of segment HA

The three triangles are all similar:
△ MTH ∼ △ MHA ∼ △ HTA
So you can set up a proportion: x / 15 = 9 / x

Then x2 = 135 and x = 3 sqrt(15) cm
The use the Pythagorean Theorem to solve for HM and HT


Correctly solved by:

1. Colin (Yowie) Bowey Beechworth, Victoria, Australia
2. Dr. Hari Kishan D.N. College,
Meerut, Uttar Pradesh, India
3. Veena Mg Bangalore, Karnataka, India
4. Davit Banana Istanbul, Turkey
5. K. Sengupta Calcutta, India
6. Ritwik Chaudhuri Santiniketan, West Bengal, India
7. Ivy Joseph Pune, Maharashtra, India
8. Kelly Stubblefield Mobile, Alabama