Geometry
# Properties of Triangles

If \(x=\sqrt{6}\) and \(y=\sqrt{10}\) in right triangle \(\triangle ABC\) shown in the diagram above, what is the length of \(\overline{AC} ?\)

**Note:** The above diagram is not drawn to scale.

Right triangle \(ABC\) has side lengths \(N+1, N-1,\) and \( \frac {N}{2}.\)

What is the value of \(N?\)

In the figure above, if \(l_1=10,\) \(l_2=8\) and \(\alpha=\beta={56}^\circ,\) what is the value of \(x ?\)

**Note:** The above diagram is not drawn to scale.

As shown in the above diagram, Raj folded a rectangular paper \(ABCD\) with side length \(\overline{AD} = 5 \) in such a way that vertex \(D\) falls on side \(AB\) and is labeled point \(F.\) If the length of \(\overline{AF}\) is \(2,\) what is the length of \( \overline{DE}?\)

**Note:** The above diagram is not drawn to scale.

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