8. The perimeter of a triangular garden is 900 cm and its sides are in the ratio 3: 5: 4. Using Heron's formula, find the
area of triangular garden.
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Step-by-step explanation:
Sum of all the sides of a triangle = perimeter
3x + 5x + 4x = 900
12x = 900
x = 900/12
x = 75
So, measures of sides of triangle are 225, 375 and 300.
Semi perimeter of a triangle = 450 cm
Area of triangle = under root s × (s-a) × (s-b) × ( s-c)
= under root 450 × (450-225) × (450-375) × (450-300)
= under root 450 × 225 × 75 × 150
= √1139062500
= 33750 cm^2
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