Two corners of an isosceles triangle are at #(2 ,6 )# and #(4 ,8 )#. If the triangle's area is #36 #, what are the lengths of the triangle's sides?
1 Answer
The length of the sides are
Explanation:
The length of side
Let the height of the triangle be
The area of the triangle is
The altitude of the triangle is
The mid-point of
The gradient of
The gradient of the altitude is
The equation of the altitude is
The circle with equation
The intersection of this circle with the altitude will give the third corner.
We solve this quadratic equation
The points are
The length of
graph{(y+x-10)((x-2)^2+(y-6)^2-0.1)((x-4)^2+(y-8)^2-0.1)((x-3)^2+(y-7)^2-648)=0 [-52.4, 51.64, -21.64, 30.4]}