Question

sides of a triangular field are in the ratio of 4:5:6 then find the area of the fiels if its perimeter is 300m​

Answer 1

Answer:

$\bf\huge\red{\mid{\overline{\underline{AnswEr}}}\mid}$

Let the sides be 4x,5x and 6x .

4x + 5x + 6x = 300m

15x = 300m

x = 15/300 = 20

=> 4x = 4×20=80m ; 5x = 5×20=100m ; 6x = 6×20=120m

Area of ∆ = √s ( s-a ) ( s-b ) ( s-c )

=> S = 300/2 = 150 ; S-a = 150 - 80 = 70 ; s - b = 150 - 100 = 50 ; s - c = 150 - 120 = 30

Area of ∆ = √150 × 70 × 50 × 30

=> √5 × 3 × 5 × 2 × 7 × 5 × 2 × 5 × 5 × 2 × 3 × 5 × 2

=> 5 × 5 × 5 × 5 × 2 × 2 × 3√7

=> 150√7m²

Hope it helps !

Answer 2

Answer:

Let the sides be 4x,5x and 6x .

4x + 5x + 6x = 300m

15x = 300m

x = 15/300 = 20

=> 4x = 4×20=80m ; 5x = 5×20=100m ; 6x = 6×20=120m

Area of ∆ = √s ( s-a ) ( s-b ) ( s-c )

=> S = 300/2 = 150 ; S-a = 150 - 80 = 70 ; s - b = 150 - 100 = 50 ; s - c = 150 - 120 = 30

Area of ∆ = √150 × 70 × 50 × 30

=> √5 × 3 × 5 × 2 × 7 × 5 × 2 × 5 × 5 × 2 × 3 × 5 × 2

=> 5 × 5 × 5 × 5 × 2 × 2 × 3√7

=> 150√7m²