In triangle MNP, the bisector NL is drawn. ML = 20cm, LP = 12cm MN-NP = 18. Find MNP area.
| November 29, 2020 | education
1) bis-sa divides the base into segments proportional to the sides, i.e. Np / 12 = MN / 20
2) Let x- NP, then (x + 18) -MN
3) we get:
X / 12 = (x + 18) / 20
X = 12 (x + 18) / 20
5x = 3x + 54
X = 27.
27-NP, 27 + 18 = 45 MN
According to Heron’s formula:
p = (32 + 45 + 27) / 2 = 52
S = √52 (52-32) (52-45) (52-27) = √182 000 = 20√455
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