Two sides of scalene ABC measure 3 centimeters and 5 centimeters. What is the largest possible area of the triangle?

Two sides of scalene ABC measure 3 centimeters and 5 centimeters. What is the largest possible area of the triangle?

If Δ ABC is a scalene right triangle with legs of 3 and 5 then the area is 7.5 u²  

Area = 1/2 ab*sinC\\

A=7.5sinC

The biggest sinC can be is 1 which happens when C=90degrees

So you can answer now.

You can also tell me how long the third side will be.