How do you find the dimensions of a right triangle if a right triangle has area 960 and hypotenuse length = 52?
When we solve simultaneous equations
we find no real solutions, so no such right triangle exists.
Call the legs
That's a quadratic equation in
so no real solutions for
That's the end, but we can look into it a bit deeper.
The hypotenuse is just too small to support this area. Let's find the general formula for the minimum hypotenuse for a real triangle of a given area
The discriminant must be positive or zero:
Everything is positive, so
In our case