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# Geometry

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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

### 2+0 Answers

#1
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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
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Thank you! I got it. Thanks again!

TheEarlyMathster  May 16, 2022