Question

In a rectangle if i reduce the length 5cm and increase the width 3cm then the area will be more than 9sq.cm or when i increse the length 3cm and width 2cm then the area will more than 67sq.cm.what is it's area????

Answer 1

t length of rectangle = x units and Let breadth of rectangle = y units

Area =xy square units. According to given conditions,

xy – 9 = (x − 5) (y + 3)

⇒ xy – 9 = xy + 3x − 5y – 15

⇒ 3x − 5y = 6 … (1)

And, xy + 67 = (x + 3) (y + 2)

⇒ xy + 67 = xy + 2x + 3y + 6

⇒ 2x + 3y = 61 … (2)

From equation (1),

3x = 6 + 5y

⇒ x = 

Putting this in (2), we get

2 + 3y = 61

⇒ 12 + 10y + 9y = 183

⇒ 19y = 171

⇒ y = 9 units

Putting value of y in (2), we get

2x + 3 (9) = 61

⇒ 2x = 61 – 27 = 34

⇒ x = 17 units

Therefore, length = 17 units and, breadth = 9 units