Question

the length of a rectangle exceedits width by 5 if the width is increased by 1 m and the length is decreased by 2 m the area of a new rectangle is 4 sq metre less than the area of original rectangle find the dimensions of the original rectangle

Answer 1

Let the width of original rectangle be x

=> length of original rectangle = 5 + x

=> area of original = Length × breadth

= (5 + x)x

= x² + 5x


Now new breadth = x + 1
New length = 5 + x - 2 = 3 + x

=> new area = (3 + x)(x + 1)

= 3x + 3 + x² + x

= x² + 4x + 3


Given that the new area is less than the original by 4

=> x² + 5x = x² + 4x + 3 + 4

=> x² + 5x = x² + 4x + 7

=> x² + 5x - x² - 4x = 7

=> x = 7
=> width = 7
=> original length = 5 + x = 5 + 7 = 12


So your answer

width = 7 m
Length = 12 m

Hope it helps dear friend