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.

TheEarlyMathster May 15, 2022

#1**0 **

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!!!

BuilderBoi May 15, 2022