Question

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

Answer 1

It's letter C
3sqrt2 + 2sqrt5

Answer 2

Answer: 3) is the right option. The perimeter of given isosceles trapezoid is $3\sqrt{2}+2\sqrt{5}$ units

Step-by-step explanation:

In the given diagram a isosceles trapezoid KLMN is given with sides KL= 2√2 units , LM= √5 units and MN=√2units

To find the perimeter we need all the sides of the isosceles trapezoid i.e.we need to find KN with coordinates K=(-2,-4) and N=(-1,-2),by distance formula [distance between two points =$\sqrt{(x_2-_1)^2+(y_2-y_1)^2}$]

KN=$\sqrt{(-1-(-2))^2+(-2-4)^2}\\= \sqrt{1^2+2^2}= \sqrt{1+4}= \sqrt{5}$

OR as it is a isosceles trapezoid then two of its opposite sides must have have same length. as KL≠MN then LM must be equal to KN.

Now the perimeter of KLMN=KL+LM+MN+KN= $2\sqrt{2}+\sqrt{5}+ \sqrt{2}+ \sqrt{5}\\=3\sqrt{2}+2\sqrt{5}$  units.