The shape above is a square and there is a diagonal which actually bisects the 90° angle. So, x becomes 45°. We can eliminate B and C.
The triangle which formed by the diagonal is a kind of triangle is what we know as a 45-45-90.
This triangles have the rule of "If the legs are x, the hypotenuse is x√2."
In this case the legs are 13.1; and if we knew the rule, we can say quickly that y is 13.1√2.
But let's say we forgot the rule. Now we need to use the long way: Pythogarean theorem.
[tex] {a}^{2} + {b}^{2} = {c}^{2} [/tex]
We know that a=b: [tex]2 {a}^{2} = {c}^{2} [/tex]
Isolate c by square rooting both sides: [tex]c = a \sqrt{2} [/tex]
Plug in a: [tex]c = 13.1 \sqrt{2} [/tex]
So, D is the right answer.
