Question

What value of x will make Point N the incenter of the above illustration? Solve for NM by drawing a picture and using the NM = V252 - 152. Then set NM = LN to solve for x.

LN = 5x
DN = 25
DM = 15
To make N be the incenter the value of x=_____.
(format is numeric to the one's place)
(Segment NL - Segment NM = Segment NK)

Answer 1

To find the value of x that will make Point N the incenter of the illustration, use the equation NM = LN and solve for x.

Step-by-step explanation:

To find the value of x that will make Point N the incenter of the illustration, we can use the fact that the incenter is equidistant from the three sides of the triangle. Let's start by setting up an equation using the given information:

LN = 5x

DN = 25

DM = 15

We can use the formula NM = sqrt(LN*DN) - sqrt(LN*DM) to find the value of NM. Plugging in the values, we get:

NM = sqrt(5x*25) - sqrt(5x*15)

Then, we can use the equation NM = LN to solve for x. So, we can set up the equation:

sqrt(5x*25) - sqrt(5x*15) = 5x

Simplifying and solving this equation will give us the value of x that makes Point N the incenter of the illustration.