Question

in the diagram, kl = 2√2, lm = √5, and mn = √2. what is the perimeter of isosceles trapezoid klmn? ○ √2 units ○ √5 units ○ 3√2 + 2√5 units ○ 4√2 + 2√5 units

Explanation:

Step1: Recall perimeter of trapezoid

Perimeter of a trapezoid is the sum of all its sides. For isosceles trapezoid KLMN, sides are \( KL \), \( LM \), \( MN \), and \( NK \). Since it's isosceles, \( LM = NK \).

Step2: Identify given and equal sides

Given \( KL = 2\sqrt{2} \), \( LM = \sqrt{5} \), \( MN = \sqrt{2} \), and \( NK = LM=\sqrt{5} \) (isosceles trapezoid property).

Step3: Calculate perimeter

Perimeter \( P = KL + LM + MN + NK \)
Substitute values: \( P = 2\sqrt{2}+\sqrt{5}+\sqrt{2}+\sqrt{5} \)
Combine like terms: \( P=(2\sqrt{2}+\sqrt{2})+(\sqrt{5}+\sqrt{5}) = 3\sqrt{2}+2\sqrt{5} \)

Answer:

\( 3\sqrt{2} + 2\sqrt{5} \) units (corresponding to the option " \( 3\sqrt{2} + 2\sqrt{5} \) units")