Question

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 HELP.

Answer 1

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 $\frac{7}{11}$