Answer:
a. The distance from the library to the park is 2√5 miles
b. The distance from the park to the football field is 2√35 miles
The last answer ⇒ 2√5 miles , 2√35 miles
Step-by-step explanation:
* Lets revise the rules in the right angle triangle when we draw the
perpendicular from the right angle to the hypotenuse
- In triangle ABC
# Angle B is a right angle
# The hypotenuse is AC
# BD ⊥ AC
∴ (AB)² = AD × AC
∴ (BC)² = CD × AC
∴ (BD)² = AD × CD
∴ BD × AC = AB × BC
* Lets use one of these rules to solve the problem
- Vertex B represents the position of the park
- Vertex A represents the position of the home
- Vertex C represents the position of the football field
- Vertex D represents the position of the library
- AB represents the distance from the home to the park
- CB represents the distance from the football field to the park
- DB represents the distance from the library to the park
- AC represents the distance from the home to the football field
- AD represents the distance from the home to the library
- CD represents the distance from the football field to the library
* Now lets solve the problem
a.
∵ The distance from the home to the library is 4 miles
∴ AD = 4
∵ The distance from the football field to the library is 10 miles
∴ CD = 10
∵ The distance from the library to the park represented by BD
- Lets use the rule (BD)² = AD × CD
∴ (BD)² = 4 × 10 = 40 ⇒ take √ for both sides
∴ BD = √40 = 2√5 miles
* The distance from the library to the park is 2√5 miles
b.
∵ The distance from the park to the football field represented by BC
* Lets use the rule (BC)² = CD × AC
∵ CD = 10
∵ AC = 4 + 10 = 14
∴ (BC)² = 10 × 14 = 140 ⇒ take √ for both sides
∴ BC = √140 = 2√35 miles
* The distance from the park to the football field is 2√35 miles
