Based on the property of similar triangles the distance BE is 173.86 feet and PE is 153.40.
What is similar triangle?
Two triangles are similar if they have the same ratio of corresponding sides and equal pair of corresponding angles. Similar triangles are the triangles that are the same in shape, but may not be equal in size.
For the given situation,
The diagram shown has different line segments.
Let GCPR be parallelogram, so opposite sides and opposite angles are equal.
So, [tex]GC=RP[/tex]
⇒ [tex]RP=375[/tex]
Then, [tex]RG=CB+BP[/tex]
⇒ [tex]RG=325+225[/tex]
⇒ [tex]RG=550[/tex]
Now consider the triangle ΔGER, based on the property of similar triangles,
a) [tex]\frac{GR}{BP} =\frac{GB}{BE}[/tex]
⇒ [tex]\frac{550}{225} =\frac{425}{BE}[/tex]
⇒ [tex]BE=\frac{(425)(225)}{550}[/tex]
⇒ [tex]BE =173.86[/tex]
b) [tex]\frac{GR}{BP} =\frac{RP}{PE}[/tex]
⇒ [tex]\frac{550}{225} =\frac{375}{PE}[/tex]
⇒ [tex]PE=\frac{(375)(225)}{550}[/tex]
⇒ [tex]PE=153.40[/tex]
Hence we can conclude that based on the property of similar triangles the distance BE is 173.86 feet and PE is 153.40.
Learn more about similar triangles here
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