+273 In triangle ABC, AB = 10, BC = 24, and AC = 26. Find the length of the shortest altitude in this triangle.
I think its a right triangle, but don't know how to use that information to solve the problem.
+2668 It is indeed a right triangle, and the shortest altitude will be perpendicular to the hypotenuse.
The area of the triangle is \(10 \times 24 \div 2 = 120\).
Because the altitude is perpendicular to the hypotenuse, we know that \(\text{hypotenuse} \times\text {altitude} \div 2 = [\text{ABC}]\). Think of the hypotenuse as the base, and the altitude as the height.
Subsituting what we know, we have: \(26 \times \text{altitude} \div 2 = 120\), and we can solve for the altitude.
Hope this helps!!!
