The area of a rectangle is 48 square centimeters if the leng

The area of a rectangle is 48 square centimeters. if the length and width are each increased by 4 centimeters, the area of the newly formed rectangle is 120 square centimeter. Find the dimensions of the original retangle.

Solution

Let the length of the rectangle = x

and width of the rectangle = y

Then we have xy = 48.......................(1)

Now when we changed the dimension

new length = x+4

and new width = y+4

Hence new area

A= (x+4) (y+4) = 120

=> xy + 4x+4y +16 = 120

=> 48 + 4x + 4(48/x) +16 = 120

=> 4x+ 192/x +64 = 120

=> x+ 48/x +16 = 30

=> x^2 +48 +16x = 30x

=> x^2 - 14x +48 =0

=> x^2 -8x-6x +48 =0

=> (x-8) (x-6) = 0

=> x= 8, 6

when x= 8 , y= 48/8 = 6

when x= 6 , y= 48/6 = 8