# Two corners of an isosceles triangle are at #(2 ,3 )# and #(1 ,4 )#. If the triangle's area is #64 #, what are the lengths of the triangle's sides?

##### 1 Answer

Oct 21, 2016

The 3 sides are

#### Explanation:

Let b = the length of the base from

This cannot be one of the equal sides, because the maximum area of such a triangle would occur, when it is equilateral, and specifically:

This conflicts with our given area,

We can use the Area to find the height of the triangle:

The height forms a right triangle and bisects the base, therefore, we can use the Pythagorean theorem to find the hypotenuse: