Geometry
# Properties of Triangles

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

If**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 $N?$

$l_1=10,$ $l_2=8$ and $\alpha=\beta={56}^\circ,$ what is the value of $x ?$

In the figure above, if**Note:** The above diagram is not drawn to scale.

$ABCD$ 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 $\overline{DE}?$

As shown in the above diagram, Raj folded a rectangular paper**Note:** The above diagram is not drawn to scale.