Question

In the diagram, KL = , LM = , and MN = . What is the perimeter of isosceles trapezoid KLMN?

Answer 1

The trapezoid is isosceles. Thus, the bases are $\overline{KL}$ and $\overline{NM}$, while the equal sides are $\overline{LM}$ and $\overline{KN}$.

This also means that the length of the sides $\overline{LM}$ and $\overline{KN}$ are equal.


The perimeter of the trapezoid is the sum of the lengths of the sides of the trapezoid, so the perimeter is:

$KL+LM+MN+NL=2 \sqrt{2}+ \sqrt{5}+ \sqrt{2}+\sqrt{5}=3 \sqrt{2}+2 \sqrt{5}.$


Answer: third choice