In △abc, points m and p are points on sides ac and bc respectively. find the area of △mpc, if bm∩ap=o, aaom=45 dm2, abop=15 dm2, and aaob=75 dm2. i will give you brainliest pls .

First calculate the Area of MOP by using congruent altitudes.

(Area MOP)/(Area AOM) = PO/OA = (Area BOP)/(Area AOB)

Area MOP = (Area AOM)*(Area BOP)/(Area AOB) = (45)*(15/75) = 9.

Now, let Area CMP = x. And use two sets of triangles with congruent altitudes.

(Area CMP)/(Area BMP) = x/(9+15) = x/24 = (CP)/(BP).

(Area CAP)/(Area BAP) = (x+54)/90 = (CP)/(BP)

So,

(Area CMP)/(Area BMP) = (Area CAP)/(Area BAP)

or

x/24 = (x+54)/90

90x = 24 (x+54) = 24x + 1296

66x = 1296

x = 19

8

step-by-step explanation: