Answer:
The length of the side along the river is 140 m
Step-by-step explanation:
Equations
To solve the problem, we need to recall the area of a trapezium is:
[tex]\displaystyle A=\frac{b1+b2}{2}.h[/tex]
Where b1 and b2 are the lengths of the parallel sides and h is the height of the trapezium.
The field to be bought by Mohan has a trapezium shape with a side along the road of side x and a side along the river of side 2x, as stated in the problem.
Knowing the height is h=100 m, and the area is 10500 m2:
[tex]\displaystyle \frac{x+2x}{2}\cdot 100=10500[/tex]
Simplifying:
[tex]\displaystyle (3x)\cdot 50=10500[/tex]
[tex]150x=10500[/tex]
Dividing by 150:
[tex]x = 10500 / 150 = 70[/tex]
x = 70 m
2x = 140 m
The length of the side along the river is 140 m
