Question

A rectangle is 14 cm long and 10 cm wide. If the length is reduced by x cm and its width is increased also by x cm so as to make it a square then its area changes by

Answer 1

Answer:

Area is increased by 4 cm^2

Step-by-step explanation:

Ori. length = 14  ; Ori. breadth = 10

     Now, length is reduced by x and width is increased by x, now,

New len. = 14 - x  ;  New bre. = 10 + x

      In square, all sides are equal.

⇒ New length = new breadth

⇒ 14 - x = 10 + x

⇒ 14 - 10 = 2x       ⇒ 4 = 2x

⇒ 2 = x

          Hence,

Side of square = 14 - 2 = 12 cm

Thus, change in area:

            = area of squ. - area of rect.

            = (12)^2 - (14 * 10)

            = 144 - 140

            = 4

Means, area is increased by 4 cm^2