Question

A farmer has 70 m of fencing ,with which he encloses three sides of a

rectangular sheep pen, the fourth side being a wall. If the area of the pen is 600

sq. m. Find the length of it’s shorter side.​

Answer 1

Answer:

Step-by-step explanation:

Let the length and breadth of the rectangular sheep pen be x and y respectively. From the given information,

x + y + x = 70

2x + y = 70 ... (1)

Also, area = xy = 600

Using (1), we have:

x (70 − 2x) = 600

70x − 2x2 = 600

2x2 − 70x + 600 = 0 divide by 2)

x2 − 35x + 300 = 0

Factorising

x2 − 15x - 20x + 300 = 0

x(x − 15) − 20(x − 15) = 0

(x − 15)(x − 20) = 0

x = 15, 20

If x = 15, then y = 70 - 2x = 70 − 30 = 40 m

If x = 20, then y = 70-2×20

=70-40 = 30 m

Hence shorter side is 30 m