If IJ=11, JK=10, IK=13, MN=12, and LN=15.6, find the perimeter of triangle, L, M, N△LMN. Round your answer to the nearest tenth if necessary. Figures are not necessarily drawn to scale
To find the perimeter of triangle LMN, we need to find the length of LM.
We can start by applying the Pythagorean theorem to triangle IJN, using IJ = 11 and IK = 13. Let's call the length of NJ as x:
IJ^2 + NJ^2 = IJ^2
11^2 + x^2 = 13^2
121 + x^2 = 169
x^2 = 169 - 121
x^2 = 48
x ≈ √48
x ≈ 6.9 (rounded to the nearest tenth)
Next, we know that LN = 15.6, and we have found that NJ ≈ 6.9. To find LM, we can subtract the length of NJ from LN:
LM = LN - NJ
LM = 15.6 - 6.9
LM ≈ 8.7 (rounded to the nearest tenth)
Finally, to find the perimeter of triangle LMN, we can add up the lengths of all three sides:
Perimeter = LM + MN + LN
Perimeter = 8.7 + 12 + 15.6
Perimeter ≈ 36.3 (rounded to the nearest tenth)
Therefore, the perimeter of triangle LMN is approximately 36.3.