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Answer:
The area of the triangular garden is 33750 cm²
Step-by-step explanation:
Let us use Heron's Formula for the area of a triangle
, where
- a, b, and c are the lengths of the three sides of the triangle
∵ The perimeter of a triangular garden is 900 cm
∴ The sum of the lengths of its three sides = 900 cm
∵ Its sides are in the ratio 3 : 5 : 4
→ Let us use the ratio method to find the length of its sides
→ S1 : S2 : S3 : perimeter
→ 3 : 5 : 4 : 12 ⇒ (3 + 5 + 4)
→ a : b : c : 900
→ By using cross multiplication
∵ a × 12 = 3 × 900
∴ 12a = 2700
→ Divide both sides by 12
∴ a = 225 cm
∵ b × 12 = 5 × 900
∴ 12b = 4500
→ Divide both sides by 12
∴ b = 375 cm
∵ c × 12 = 4 × 900
∴ 12c = 3600
→ Divide both sides by 12
∴ c = 300 cm
Now let us use Heron’s formula, to find the area of the triangular garden
∵
∵ a = 225, b = 375, c = 300
∴
∴ p = 450
∵
∴ A = 33750 cm²
∴ The area of the triangular garden is 33750 cm²