Question

a farmer 70 m of fencing with which he encloses three sides of rectangular shape pen, the forth side is being a wall. If the area of a pen is 600 sq.m find the length of the shorter side

Answer 1

Answer:

Let the length of rectangle pen be x and breadth be y respectively.

According to the given condition we get,

x + y + x = 70

2x + y = 70 ---[1]

The area of a Rectangular pen is 600 sq. m

Area of rectangle = Lenght × breadth

= xy = 600 sq. m

From equation [1],

x( 70 - 2x) = 600

70x - 2x^2 = 600

2x^2 − 70x + 600 = 0

x^2 − 35x + 300 = 0

x^2 − 15x - 20x + 300 = 0

x(x − 15) − 20(x − 15) = 0

(x − 15)(x − 20) = 0

Therefore, x = 15 & x = 20

If we take x = 15 Substituting in equation [1]

2(15) + y = 70

30 + y = 70

y = 70 - 30

y = 40

If we take x = 20 Substituting in equation [1]

2(20) + y = 70

40 + y = 70

y = 70 - 40

y = 30

Therefore, the length of shorter side is 15 if longer side is 40 and if the longer side is 30 the shorter side is 20.