Question

the perimeter of a triangular field is 250 m and its sides are in ratio 7:8:10.find the area of the triangular field using herons formula

Answer 1

let the sides be 7x,8x and 10x. perimeter of a triangular field =250 m=7x+8x+10x=> 250=25x=>
x=10 m So sides are 70m,80m and 100m. Area of a triangle with sides of length a,b,c =√s(s-a)(s-b)(s-c) where s=a+b+c/2. So the Area of the triangle=
√125(125-70)(125-80)(125-100) =√125×55×45×25 =
√625×9×25×55= √625×√9×√25×√55 =25×3×5×√55 =375√55 =375(7.416)=2781 square metre .

Answer 2

Let the sides be 7x,8x and 10x

Perimeter= Sumof all sides

Perimeter=7x+8x+10x

250m=25x

X=10m

one side = 7*10=70m
2nd side = 8*10=80m
3re side = 10*10=100m

semi perimeter (s) = 250/2=125m

Heron's formula

Area =√s(s-a)(s-b)(s-c)
Area=√125(125-70)(125-80)(125-100)
Area=√125*55*45*25
Area=5*5*5*3√11*5
Area=375√55

So the area is 375√55 m²