Question

How many kilometers is it from the main gate to Manatee Springs? (Hint: To convert from

yards to kilometers, multiply by 0.0009144). Round answer to the nearest hundredth kilometer.

Answer 1

Distance between Main gate M and manatee Spring S,

MS = 6.035 km ≅ 6 km (rounded off)

Explanation:

Let the point at Train depot be T. Point at Main gate be M. Point at Bird sanctuary be B. Point at Elephant house be E. Point at manatee Springs be S.

Now, we have two triangles TMB and TSE.

From figure given that, ∠MTB = ∠STE

∠TMB = ∠TSE

∠TBM = ∠TES.

⇒ From AAA similarity, Triangles TMB and TSE are similar.

⇒
`(TM)/(TS) = (TB)/(TE)`

⇒
`(x)/(4200) = (2000)/(3500)`

⇒ x = 2400 yds

⇒ Distance between Main gate M and manatee Spring S,

MS = MT + TS = x + 4200 = 2400 + 4200 = 6600 yds

⇒ MS = 6600 yds = 6600 × 0.0009144 km = 6.035 km ≅ 6 km