Hey everyone, would appreciate some help with this question. Please let me know the working alongside the answer. Thanks
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The answer is A. y > 21/2
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
y2 >2
y > 21/2
Let y = x, to find the smallest value y can be.
Solve for 1/2 x2 = 1
x2 = 2, x = \sqrt{2}
y > x therefore y > \sqrt{2}