# How do you find the dimensions of a right triangle if a right triangle has area 960 and hypotenuse length = 52?

##### 1 Answer

#### Answer:

When we solve simultaneous equations

we find no real solutions, so no such right triangle exists.

#### Explanation:

Call the legs

Let's eliminate

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