Question

Given the image below, ⎯⎯⎯⎯⎯⎯⎯⎯⎯,⎯⎯⎯⎯⎯⎯⎯⎯,⎯⎯⎯⎯⎯⎯⎯⎯DY¯,EY¯,FY¯ are perpendicular bisectors of △△ABC.

Answer 1

Remember that

A perpendicular bisector divides a segment into two equal parts

so

AD=DB=61.7

In the right triangle DYB

Apply the Pythagorean Theorem

`YB^2=DY^2+DB^2`

where

YB=64.2

DB=61.7

substitute given values

`\begin{gathered} 64.2^2=DY^2+61.7^2 \\ DY^2=64.2^2-61.7^2 \\ DY^=17.74 \end{gathered}`

Find out the value of EB

In the right triangle YEB

Apply the Pythagorean Theorem

`YB^2=YE^2+EB^2`

where

YB=64.2

YE=51.2

substitute given values

`\begin{gathered} 64.2^2=51.2^2+EB^2 \\ EB^2=64.2^2-51.2^2 \\ EB=38.73 \end{gathered}`