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The perpendicular bisectores of the sides of triangle JLo intersect at point p. If 2x+5 meters and KP = 4x-13 meters, what’s the length of LP to the nearest meter

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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?

User Eugene Chow
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