The two legs of an isosceles triangle have length y. What is the maximum area that the triangle can have? Express your answer in terms of y.
Note that the area of a triangle can be given by
(1/2) (side A) (side B) ( sine of included angle between sides A, B)
And note that the sine is greatest at 90° = 1
So.....the max area is
(1/2) (y) (y) sin (90°) =
(1/2)y^2 (1) =