Question

The cost of fencing a triangular plot with sides in the ratio 5:12:13 is rupees 25 per metre. If the total cost incurred to fence the plot is rupees 2250,then the area of the plot is​

Answer 1

Answer:

270 m²

Step-by-step explanation:

given perimeter of ∆ = 2250/25 = 90 m

let the sides of ∆ be 5x, 12x and 13

perimeter of ∆ = side1 +side2 +side3 = 5x + 12x + 13x = 30x

30x = 90

x = 90/30

x = 3m

now side1 = 5x = 5×3 = 15m

side2 = 12x = 12×3 = 36m

side3 = 13x = 13×3 =39m

semiperimeter = perimeter/2 = 90/2 = 45m

area of ∆ =

$\sqrt{[s(s-a)(s-b)(s-c)]}$

$= \sqrt{[45(45-15)(45-36)(45-39)}$

$= \sqrt{[45(30 \times 9 \times 6)]}$

$= \sqrt{72900}$

= 270 m²