Math CentralQuandaries & Queries


Question from devon, a student:

hay ok i have the height of a triangle but how do i find the length of the side if all of the sides are the same length

Hi Devon,

Suppose the triangle is ABC and the length of each side is a units. If you draw a line from A to meet the line BC at D and this line is perpendicular to BC then the length of AD is the height h of the triangle.


The point D is the midpoint of BC (do you see why?) and hence the length of DC is a/2. Since triangle ADC is a right triangle you can use Pythagoras' theorem to find a.


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