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 √(2)+ √(5)+ √(2)+√(5)=3 √(2)+2 √(5).`


Answer: third choice