Hey everyone, would appreciate some help with this question. Please let me know the working alongside the answer. Thanks

Which video is this from?

Can you share the link?

The answer is A. y > 2^{1/2}

An easy way is to just plug in numbers. You’ll see that A is the only one that holds. For example, x = 1, y = 2

Formal method:

We are given that x < y < z and that this is a right-angle triangle. It follows that z is hypotenuse since it is the largest side.

Now, given that the area of the triangle is 1, this imples that:

\frac{1}{2}xy = 1

=> xy = 2

=> x= \frac{2}{y}

Now, we know that y > x, plugging in:

y > x

y > 2/y

y^{2} >2

y > 2^{1/2}

Let y = x, to find the smallest value y can be.

Solve for 1/2 x^{2} = 1

x^{2} = 2, x = \sqrt{2}

y > x therefore y > \sqrt{2}