Question

Side AC and side BD are perpendicular bisectors of each other. Find BC and DB

A. BC = 12, DB = 24

B. BC = 13, DB = 12

C. BC = 13, DB = 24

D. BC = 12, DB, 13

Answer 1

The answer is BC=13 and DB=24

Answer 2

(C)BC = 13, DB = 24

Explanation:

It is given that Side AC and side BD are perpendicular bisectors of each other, then from the figure, we have

DE=EB=12(Side AC and side BD are perpendicular bisectors of each other)

Now, from ΔBEC, we have

`(BC)^2=(BE)^2+(EC)^2`

=
`(12)^2+(5)^2`

=
`144+25`

=
`169`

Therefore, BC=
`√(169)=13`

Thus, BC=13

Also, DB=DE+EB

DB=12+12

DB=24

Therefore, BC = 13, DB = 12