Applying the perpendicular bisector of a triangle's property, the length of LP to the nearest meter is: 23 meters.
What is a perpendicular bisector of a triangle?
The perpendicular bisector of a side of a triangle bisects that side and is perpendicular to it. The point where all three perpendicular bisectors of a triangle meet is the circumcenter, and this means that they are all equidistant from this point.
Since point p in triangle JKL is the point where all the three perpendicular bisectors meet, therefore, JP = KP. Set the expressions for JP and KP equal to each other:
2x + 5 = 4x - 13
Now, solve for x:
2x + 5 = 4x - 13
18 = 2x
18/2 = x
9 = x
x = 9
Substitute the value of x back into either JP or KP. Let's use JP:
JP = 2x + 5
JP = 2(9) + 5
JP = 18 + 5
JP = 23
So, the length of LP = JP which is also 23 meters.
Complete Question:
The perpendicular bisectors of the sides of △ JKL intersect at point P. If JP = 2x + 5 meters and KP = 4x - 13 meters, what is the length of LP to the nearest meter?