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
[tex]A=\sqrt{p(p-a)(p-b)(p-c)}[/tex], where
∵ 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
∵ [tex]p=\frac{a+b+c}{2}[/tex]
∵ a = 225, b = 375, c = 300
∴ [tex]p=\frac{225+375+300}{2}=\frac{900}{2}[/tex]
∴ p = 450
∵ [tex]A=\sqrt{450(450-225)(450-375)(450-300)}[/tex]
∴ A = 33750 cm²
∴ The area of the triangular garden is 33750 cm²
