Two corners of an isosceles triangle are at #(1 ,2 )# and #(3 ,1 )#. If the triangle's area is #2 #, what are the lengths of the triangle's sides?
1 Answer
Find the triangle's height and use Pythagoras.
Explanation:
Start by recalling the formula for the height of a triangle
The given corners can produce one side, which we will call the base. The distance between two coordinates on the XY plane is given by the formula
Now we need to find the side. Noting that drawing the height inside an isosceles triangle makes a right triangle consisting of half of the base, the height and the leg of the full triangle, we find that we can use Pythagoras to calculate the hypotenuse of the right triangle or the leg of the isosceles triangle. The base of the right triangle is