Question

The length of a rectangle exceeds its breadth by 7 cm. If the length is decreased by 4 cm and the breadth is increased by 3 cm, the area of the new rectangle is the same as the area of the original rectangle. Find the length and the breadth of the original rectangle.

Answer 1

To Find: Length and Breadth of the original rectangle'Let the length and breadth of a rectangle be l cm and b cm

According to the question

Breadth of rectangle is 7 less than the length of the rectangle,

l - 7 = b ......(1)

Area of a rectangle = (l × b)

Now length of the rectangle is decrease by 4, and breadth increased by 3,

Area of new rectangle = (l - 4)(b + 3)

Area of new rectangle = Area of Old rectangle(l - 4)(b + 3) = lb

Now

Putting the value of b from equation 1, we get,

(l - 4)(l - 7 + 3) = l(l - 7)

(l - 4)(l - 4) = l(l - 7)Opening the brackets, we get,

⇒ l² - 4l - 4l + 16 = l2 - 7l

⇒ l² - 8l + 16 = l2 - 7l

⇒ - l = - 16

⇒ l = 16 cm

b = l - 7 = 16 - 7 = 9 cm

Hence, length and breadth of original rectangle are 16 cm and 9 cm.