Kendra lives 10 Km from the northern tip of swan lake and 6 Km from the southern tip of swan lake. What is the north - south distance across swan lake?

The north - south distance across swan lake is 8 km

Step-by-step explanation:

Look to the attached figure

Kendra's house and the distances between it and the North tip, southern tip of swan lake formed a right Δ

∵ Kendra lives 10 Km from the northern tip of swan lake

- That means the length of the hypotenuse of the right Δ is 10

∴ The hypotenuse of the right Δ = 10

∵ Kendra lives 6 Km from the southern tip of swan lake

- That means the length of the horizontal leg of the right Δ is 6

∴ The horizontal leg = 6

- By using Pythagoras Theorem

∵ (hypotenuse)² = (H.leg)² + (V.leg)²

∴ (10)² = (6)² + (x)²

∴ 100 = 36 + x²

- Subtract 36 from both sides

∴ 64 = x²

- Take √  for both sides

∴ 8 = x

∴ The vertical leg of the right triangle = 8

∵ x represents the north-south distance across swan lake

∴ The north - south distance across swan lake is 8 km