Question

A farmer has a field in shape of a right triangle with legs of lengths 128 m and 64 m. He wants to leave a space in the form of a square of largest size inside the field for growing wheat and the rest for growing vegetables. Find the length of the side of such a square space. what value is indicated from this action?

Answer 1

Solution:-
Let the side of square be 'x' m
In triangle ABC
tan C = AB/BC = 64/128 = 1/2
In triangle CDE 
tan C = DE/CE
1/2 = x/(128-x)
128 - x = 2x
3x = 128
x = 128/3
x= 42.66 m
So, side of the square space is 42.66 m  Answer.
The value indicated in this action is that the farmer has tried to produce cereals as well as vegetables because both are required for the people.

Answer 2

See the Diagram.
 
 ABC is the field of the farmer.       a = 64m      b = 128 m

ADEF is the square of largest size. E has to be on BC for the square to be the largest. We need to find  AD = DE = x.

We see that     DB || FE ,   DE || FC,   and  BE || EC.
So Δ DBE and Δ FEC are similar.

CF / FE  =  ED / DB
=>    (b - x) / x  =  x / (a - x)
=>    ab + x² - (a+b) x = x²
=>    x = a b/ (a+b)  = side of the maximum square
=>    x = 64 * 128 / (64 + 128)   meters
           = 128/3 = 42.67  meters.

   This action of using agricultural field for growing multiple crops is good to take advantage of the different nutrients in the soil. It also helps to produce seeds and vegetables for self use and for use of society.  The is income on regular basis (short term) from vegetables. There is income on long term basis from wheat

   Also the social needs of people for multiple produces and not just profit oriented farming is shown by the farmer.