A right triangle has a short side of 6 and a hypotenuse of 16. What is the length of the third side? (In square root)

The original are would be 48.

Since we know that the length and width are two consecutive even integers, we can model them as follows:

Width = x

Length = x + 2

This works because no matter what even number is put in for x, the length will also be even.

Now we know if we subtract 3 from the width, we have a new rectangle that gives us an area of 24 inches. Therefore, our new triangle has the following:

Width: x - 3

Length: x + 2

Area: 24

And we can plug this into the equation.

Length* Width = Area

(x + 2)(x - 3) = 24

x^2 - x - 6 = 24

x^2 - x - 30 = 0

This is not a quadratic that we can factor to show the following:

(x - 6)(x + 5) = 0

This gives us the answers of x = 6 and x = -5. Since a side can't be negative, we throw out the x = -5 and the answer is x = 6.

So if we go back to the original rectangle, we know:

Width = x = 6

Length = x + 2 = 8

Area = 6*8 = 48