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.
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
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