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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.

 May 15, 2022
 #1
avatar+1750 
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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!!!

 May 15, 2022
 #2
avatar+250 
+1

Thank you! I got it. Thanks again!

TheEarlyMathster  May 16, 2022

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