Question

The area of a rectangular field is 500 sq. m.If the length is decreased by 3m and breadth is increased by 2m it becomes a square. Find the dimensions of the rectangular field​

Answer 1

Answer:-

Let the length of the field be "L" and it's breadth be "B".

Given:

Area of the field = 500 m²

We know that,

Area of a rectangle = length*breadth

Hence,

→ LB = 500

→ L = 500/B -- equation (1)

And,

If the length is decreased by 3 m and breadth is increased by 2 m it becomes a square.

→ L - 3 = B + 2

(Since , all the sides of a square are equal)

Putting the value of "L" from equation (1) we get,

→ 500 / B - 3 = B + 2

→ (500 - 3B) / B = B + 2

On cross multiplication we get,

→ 500 - 3B = B (B + 2)

→ 500 - 3B = B² + 2B

→ B² + 2B + 3B - 500 = 0

→ B² + 5B - 500 = 0

→ B² - 20B + 25B - 500 = 0

→ B (B - 20) + 25 (B - 20) = 0

→ (B + 25)(B - 20) = 0

→ B + 25 = 0

→ B = - 25

(or)

→ B - 20 = 0

→ B = 20

Breadth of a field can't be negative. so , Positive value is taken i.e., Breadth = 20 m

Substitute the value of "B" in equation (1)

→ L = 500/20

→ L = 25 m

Hence, the dimensions of the field are 25 m and 20 m.

Answer 2

Step-by-step explanation:

Assume that length is x and breadth is y. Then area is xy.

The area of a rectangular field is 500 sq. m. If the length is decreased by 3m and breadth is increased by 2m it becomes a square.

New length = (x - 3) m and New breadth = (y + 2) m

Area of rectangle = length × breadth

→ 500 = xy

→ x = 500/y

Also,

→ (x - 3) = (y + 2)

→ x = y + 5

→ 500/y - y = 5

→ 500 - y² = 5y

→ y² + 5y - 500 = 0

→ y² + 25y - 20y - 500 = 0

→ y(y + 25) -20(y + 25) = 0

→ (y - 20)(y + 25) = 0

→ y = 20 , -25 (negative one neglected)

Now,

→ x = 500/20

→ x = 25

Hence, length is 25 m and breadth is 20 m.