Question

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

Answer 1

$let \: breath = x \\ length = x + 7 \\ now \: b = x + 3 \\ l = x + 3 \\ {x}^{2} + 7x = {x}^{2} + 6x + 9 \\ x = 9 \\ therefore \: breath = 9cm \\ length = 9 + 7 = 16cm$

Answer 2

Answer:

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.