Find KN and LM. In triangle LKM, angle L is bisected. Line segment LK is 11, line segment KN is x-4, line segment NM is 5.4, and line segment LM is 2x + 1.3
(there is a drawing of this triangle)
Thanks.
In triangle LKM, angle L is bisected. To find the lengths of KN and LM, we can use the Angle Bisector Theorem.
According to the Angle Bisector Theorem, the ratio of the lengths of the segments that the angle bisector divides the opposite side into is equal to the ratio of the lengths of the other two sides of the triangle.
Let's denote the length of KN as a and the length of LM as b.
Using the Angle Bisector Theorem, we can set up the following equation:
LK/KN = LM/KM
Substituting the given values, we have:
11/(x-4) = (2x + 1.3)/5.4
To solve for x, we can cross-multiply:
11 * 5.4 = (x - 4) * (2x + 1.3)
59.4 = 2x^2 + 1.3x - 8x - 5.2
2x^2 - 6.7x + 64.6 = 0
Now, we can solve this quadratic equation for x by factoring, completing the square, or using the quadratic formula.
Once we find the value of x, we can substitute it back into the equations for KN and LM to find their respective lengths.