Ex 6.2, 4

Transcript

Ex 6.2, 4 The sides of a triangular plot are in the ratio 3: 5: 7; its perimeter is 300 m. Find its area. Since sides are in ratio 3: 5: 7 We can assume sides are 3x, 5x, 7x Let a = 3x, b = 5x, c = 7x Given, Perimeter = a + b + c 300 = 3x + 5x + 7x 300 = 15x 15x = 300 x = 300/15 x = 20 32 – 19 = c 13 = c c = 13 cm x = 300/15 x = 20 Thus, our sides are a = 3x = 3 × 20 = 60 m b = 5x = 5 × 20 = 100 m c = 7x = 7 × 20 = 140 m We find Area using Herons formula Area of Triangle = √(𝑠 (𝑠−𝑎)(𝑠−𝑏)(𝑠−𝑐)) Here, s = (𝒂 + 𝒃 + 𝒄)/𝟐 = 𝑃𝑒𝑟𝑖𝑚𝑒𝑡𝑒𝑟/2 = 300/2 = 150 m Now , Area of Triangle = √(𝑠 (𝑠−𝑎)(𝑠−𝑏)(𝑠−𝑐)) = √(𝟏𝟓𝟎(𝟏𝟓𝟎−𝟔𝟎) × (𝟏𝟓𝟎−𝟏𝟎𝟎) × (𝟏𝟓𝟎−𝟏𝟒𝟎)) = √(𝟏𝟓𝟎 × 𝟗𝟎(𝟏𝟓𝟎−𝟔𝟎) × (𝟏𝟓𝟎−𝟏𝟎𝟎) × (𝟏𝟓𝟎−𝟏𝟒𝟎)) = 𝑃𝑒𝑟𝑖𝑚𝑒𝑡𝑒𝑟/2 = 300/2 = 150 m Now , Area of Triangle = √(𝑠 (𝑠−𝑎)(𝑠−𝑏)(𝑠−𝑐)) = √(𝟏𝟓𝟎(𝟏𝟓𝟎−𝟔𝟎) × (𝟏𝟓𝟎−𝟏𝟎𝟎) × (𝟏𝟓𝟎−𝟏𝟒𝟎)) = √(150 × 90 × 50 × 10) = √(15 × 9 × 5 × 1 × 10,000) = √(5 × 3 × 3^2 × 5 × (100)^2 ) = √(5^2 × 3^2 × 3 × (100)^2 ) = √(5^2 ) × √(3^2 ) × √3 × √(100^2 ) = 5 × 3 × √(5^2 ) × √(3^2 ) × √3 × √(100^2 ) = 5 × 3 × √3 × 100 = 1,500√𝟑 m2