SOLUTION: A right triangle has a height 8cm more than twice the base. If the area of the triangle is 96cm^2, what are the dimensions of the triangle?

Discussion





We need to use the formula for the area of a triangle , and the

fact that the base and the height can be described one in terms of the other.







Solution





Let the short leg be x, and then the longer leg would be 2x + 8.





We are given that the area of the triangle is , so 

































 or 





Since a triangle leg with a negative length measure doesn't make much sense,

exclude the negative value.  The short leg measures 8, therefore the long leg

measures 







Check Answer





.  Answer checks.