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The lengths of the sides of a triangle are 13, 37, and 40.  Find the length of the altitude to the longest side.

 Dec 12, 2019
 #1
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Take a look at this quick sketch:

 

 Dec 12, 2019
 #2
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Obtuse scalene triangle.
Sides: a = 13 b = 37 c = 40

Area: T = 240
Perimeter: p = 90
Semiperimeter: s = 45
Calculate the heights of the triangle from its area.
There are many ways to find the height of the triangle. The easiest way is from the area and base length. The area of a triangle is half of the product of the length of the base and the height. Every side of the triangle can be a base; there are three bases and three heights (altitudes). Triangle height is the perpendicular line segment from a vertex to a line containing the base.
Height =[2 x Area] / Longest side
Height =[2 x 240] / 40 =12

 Dec 12, 2019

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