The perimeter of a triangular garden is 900cm and its sides are in the ratio 3 : 5 : 4. Using Heron’s formula, find the area of the triangular garden?

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

∵ 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

right

step-by-step explanation: