Question

I will make the right answer the brainliest, no lie.

Answer 1

Answer: The segment EF of the isoceles triangle ΔEFP is 10 units

Solution

If point P is equidistant from the vertices of ΔDEF, the segment PE must measure the same that the segment PF, then these two segments are congruent:

PE=PF

Then ΔEFP is an isisceles triangle, because it has two congruent sides (PE=PF), and the height of the side EF (PJ perpendicular to EF) divides ΔEFP into two congruent right triangles (ΔEJP and ΔFJP). The legs EJ and FJ must be congruent:

FJ=EJ

3x-1=x+3

Solving for x: Subtracting x and adding 1 both sides of the equation:

3x-1-x+1=x+3-x+1

2x=4

Dividing both sides of the equation by 2:

2x/2=4/2

x=2

Then:

FJ=3x-1→FJ=3(2)-1→FJ=6-1→FJ=5

EJ=x+3→EJ=2+3→EJ=5

EF=EJ+FJ→EF=5+5→EF=10

Answer 2

The answer is 10.  I hope this helps! ^^