Question

Mrs. Neeraj has two square plot of land with utilise for two different purpose one for providing for free education and other providing hospitilization for needy villagers. The sum of the area of 2 square plot is 5825 metre square if the difference of their perimeter is 100 metres find the sides of the two squares.

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Answer 1

Let the sides of two square land's plots are x and y respectively.
       Area of one square plot = x² m².
       Area of 2nd plot = y² m².
and,
       Perimeter of one square plot = 4.x
Perimeter of 2nd square plot = 4.y

A/Q,
        Sum of both land plot's areas = 5825 
⇒     x² + y² = 5825     --------------------------->Eqn(i)
 
and,
        Difference of their perimeters = 100
⇒     4x - 4y = 100    
⇒     4(x - y) = 100 
⇒       x - y = 100/4    
⇒        x - y = 25       --------------------------->Eqn(ii)
Taking  the square to the both side of the Eqn(ii)  
⇒    (x -  y)² = 25²
⇒     x² + y² -2xy = 625
From Eqn(i) 
⇒     5825 - 2xy = 625
⇒      2xy = 5825-625
⇒      2xy = 5200
⇒      xy = 5200/2
⇒      xy = 2600
⇒      x =  2600/y
Put the value of x in Eqn(ii)
⇒      2600/y  - y = 25
⇒     (2600 - y² )/y  = 25
⇒      2600 - y²  = 25y
⇒      y² +25y - 2600  = 0
⇒      y² +65y - 40y -2600 = 0
⇒      y(y + 65) - 40(y+65) = 0 
⇒      (y + 65)(y - 40) = 0;
⇒      y+65 = 0
         y =   -65   (Length can't be negative)
and,
        y - 40 = 0
⇒     y = 40
from Eqn(ii)
⇒      x - 40 = 25
⇒      x = 25+40
       x = 65
So sides of the Square plots are 65m and 40m.