Question

The length of a rectangular plot is 40 meters more than its
breadth. If the cost of fencing the plot at 53 per meter is Rs. 10,600,
what is the length of the plot in meters?

Answer 1

Answer:

Length = 44.49 m

Step-by-step explanation:

Let the breadth of the plot be 'b'

∴Length of the plot = (40+b)

Now perimeter of the plot = (40+b)*b

The cost of fencing the plot at 53 per meter is Rs. 10,600

∴Perimeter of the plot = 10,600/53=200m

∴(40+b)*b = 200

=> 40b+b²=200

=> b²+40b-200=0

=>b=-40±√40²-4.1.(-200)/2.1 (By quadratic formula)

=>b=-40±√1600+800/2

=>b=-40±√2400/2

=>b=(-40±20√6)/2

=>b=2(-20±10√6)/2

=>b=-20±10√6

Either b=-20+10√6

or b=-20-10√6 (not possible, because b is length hence can't be negative)

∴b=-20+10√6

=> b=-20+10*2.449 (√6=2.449)

=> b=-20+24.49

=> b=4.49 m

∴length = (40+b)= (40+4.49)= 44.49 m