Maximize area of triangle question

Hi fozzzy!

The general formula of Area can be considered as Area = (1/2)*ab sin C where C is the included angle.
The maximum would clearly be when sin C = 1 i.e. C=90 degrees. Hence a right angled traingle, as you have rightly mentioned.

For a traingle of given sides, 5 and 8, we can certainly assume that 8 be the hypotenues or we can assume 5,8 be the sides. In both the cases, we have to find which actually yeilds the max area. Incase 8 is the hypotenues, the base comes out to be approx 6 and the area is approx 15. But when 8 and 5 are the sides, the area is 20. Hence, the case where 8 and 5 are assumed sides, the area appears to be maximized. Hence we can assume the same if we are considering maximum area.

Hope it clarifies your doubt!

Regards,
A