Find the area, to the nearest cm², of the triangle whose sides are in the ratio 2 : 3 : 4 and whose

Step 1: Find actual side lengths
Ratio = 2 : 3 : 4
Let sides be 2x, 3x, 4x
Perimeter = 2x + 3x + 4x = 9x = 180
x = 20

Step 2: Calculate actual sides
Side a = 2 × 20 = 40 cm
Side b = 3 × 20 = 60 cm
Side c = 4 × 20 = 80 cm

Step 3: Find semi-perimeter
s = Perimeter/2 = 180/2 = 90 cm

Step 4: Apply Heron’s formula
Area = √[s(s – a)(s – b)(s – c)]
= √[90(90 – 40)(90 – 60)(90 – 80)]
= √[90 × 50 × 30 × 10]
= √1,350,000

Step 5: Calculate final answer
= √1,350,000
≈ 1162.0 cm²
≈ 1162 cm² (to nearest cm²)