Question

AM is the median of ΔABC. Area of ΔABC = 140 cm². AN : NC = 3 : 2. Area of ΔMNC =

Options

• 70 cm²

• 35 cm²

• 28 cm²

• 42 cm²

Answer 1

28 cm² 

Explanation:

We are given:

• ΔABC with median AM
• Area(ΔABC) = 140 cm²
• Point N on AC such that AN : NC = 3 : 2
• We are asked: Area of ΔMNC

Step 1: Recall properties

• Median AM divides ΔABC into two equal areas:
  Area(ΔABM) = Area(ΔACM) 
  = `1/2` Area(ΔABC) 
  = 70 cm²

Step 2: Consider ΔACM and ratio AN : NC

• In ΔACM, line segment MN is drawn joining M (midpoint of BC) to N on AC

• Area of ΔMNC = Fraction of ΔACM based on AN : NC = 3 : 2
  `"Area"(ΔMNC) = (NC)/(AC) xx "Area"(ΔACM)`
  = `2/5 xx 70`
  = 28 cm²