Question 1178369
The sides of the lot are in the proportion of 3:5:7.
Let the sides be 3x,5x and 7x where x is a constant.
Let the sides be a=3x, b=5x and c=7x where a,b and c are the three sides.
Area of a triangle={{{sqrt(4*a^2*b^2-(a^2+b^2-c^2)^2)/4}}}
Plugging in the values we get,
Area of the triangle={{{sqrt(4*a^2*b^2-(a^2+b^2-c^2)^2)/4}}}=sqrt(675)*(x^2/4)
Area of the triangle=2,598.08 m^2
Equating both sides we get,
sqrt(675)*(x^2/4)=2,598.08 m^2
x^2=(2598.08*4)/sqrt(675)
x^2=400.0005
x=sqrt(400.0005)=20
The value of x is 20.
The shortest side of the lot is 3x which is 60m.
Answer=60m.