Answer:
The correct answer is C. 2✓2 + 2✓5 units
Explanation:
1. Let's use the Pythagorean theorem for finding the perimeter of the kite KLMN:
A. Sides NK and KL:
Length of NK ² = 1 ² + 2² (Please note that the length of the base is 2 units and the height is 1 unit)
Length of NK ² = 1 + 4
Length of NK ² = 5
Length of NK = √5 units
Also note that the length of KL = NK, then NK + KL = 2√5 units
B. Sides MN and LM:
Length of MN ² = 1 ² + 1² (Please note that the length of the base is 1 unit and the height is 1 unit)
Length of MN ² = 1 + 1
Length of MN ² = 2
Length of MN = √2 units
Also note that the length of MN = LM, then MN + LM = 2√2 units
C. Perimeter of the kite:
Perimeter = NK + KL + LM + MN
Perimeter = √5 + √5 + √2 + √2
Perimeter = 2√5 + 2√2 units
The correct answer is C. 2✓2 + 2✓5 units