Question

Please show your work and explain

Answer 1

We can use a theorem called Proportional segments in right triangles.

1. How far is library from the park?
The perpendicular is the mean proportional between the segments of the hypotenuse, so:

`PL= √(FL \cdot HL ) = √(8 \cdot 2 ) = √(16)=4 \ miles`

2. How far is the park from the football field?
Each leg of the given triangle is the mean proportional between the hypotenuse and the adjacent segment, so:

`PF= √(FH \cdot FL ) = √((8+2) \cdot 8 ) = √(80)=4 √(5) \ miles`

Answer: A.