An isosceles triangle has sides A, B, and C, such that sides A and B have the same length. Side C has a length of #8 # and the triangle has an area of #40 #. What are the lengths of sides A and B?
Side A = Side B = 10.77 units
Let side A=side B=
Then drawing a right-angled triangle, with
Using pythagoras theorem,
But since h is a length, it can only be positive
Area of triangle =
But since x is a side, then it can only be positive
Hey, small letters for triangle sides.
Let's see if we can do this different ways. First, the way the teacher probably expects:
Let's just do it directly from Archimedes' Theorem:
The sides can be arbitrarily interchanged; I picked the form that gets some cancelling when
That was easier.