In triangle MNO, MN = 13, NO = 37. P is on MO such that NP is perpendicular to MO and NP = 12. Find the area of triangle MNO.
Please include a picture as well.
Note that triangles MNP and ONP are both right triangles
We have that
MN^2 = NP^2 + MP^2 and NO^2 = NP^2 + PO^2
13^2 = 12^2 +MP^2 37^2 = 12^2 + PO^2
169 = 144 + MP^2 1369 = 144 + PO^2
169 - 144 = MP^2 1369 - 144 = PO^2
25 = MP^2 1225 = PO^2 take the sqrt rt of both sides
5 = MP 35 = PO
Note that MP + PO = MO = 40 = the base length
So
Area = (1/2) height * base = (1/2)(NP) (MO) = (1/2) (12) (40) = 240 units^2