If IJ=11, JK=10, IK=13, MN=12, and LN=15.6, find the perimeter of triangle, △LMN. Round your answer to the nearest tenth if necessary. Figures are not necessarily drawn to scale
Solve by using cross multiplication
To find the perimeter of triangle △LMN, we need to find the lengths of LM and LN.
Since MN = 12 and LN = 15.6, LM can be found by subtracting MN from LN: LM = LN - MN = 15.6 - 12 = 3.6.
Now, let's use the given information about the ratio between the corresponding sides of triangles LNM and IJK to find the length of LK.
Since triangle LNM is similar to triangle IJK, we can write the following proportion:
LK/LN = IK/IJ
Cross-multiplying, we get LK = (IK/LN) * IJ.
Plugging in the given values, we get LK = (13/15.6) * 11 = 9.1615.
Finally, we can find the perimeter P of triangle △LMN by adding the lengths of LM, LN, and LK:
P = LM + LN + LK = 3.6 + 15.6 + 9.1615 = 28.3615.
Rounding to the nearest tenth, the perimeter of triangle △LMN is approximately 28.4.