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user100 [1]
3 years ago
13

Please show your work and explain

Mathematics
1 answer:
liberstina [14]3 years ago
4 0
We can use a theorem called Proportional segments in right triangles.

1. How far is library from the park?
<span>The perpendicular is the mean proportional between the segments of the hypotenuse, so:
</span>PL= \sqrt{FL \cdot HL } = \sqrt{8 \cdot 2 } =  \sqrt{16}=4 \ miles

2. How far is the park from the football field?
<span>Each leg of the given triangle is the mean proportional between the hypotenuse and the adjacent segment, so:
</span>PF= \sqrt{FH \cdot FL } = \sqrt{(8+2) \cdot 8 } = \sqrt{80}=4 \sqrt{5}  \ miles

Answer: A.

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