Question 1057349
Let x represent the width of the rectangle.


Since the length is 12 cm longer, the length can be represented as x + 12.


The perimeter of a rectangle is 2 times the sum of the length and the width. 


Since the perimeter of this rectangle must be 84 cm, you can write the following equation:


2(length + width) = 84


2[(x + 12) + x] = 84


Dividing both sides by 2 leaves:


(x + 12) + x = 42


Collecting and combining like terms on the left side leaves:


2x + 12 = 42


Subtracting 12 from both sides then gives:


2x = 30


Dividing both sides by 2 gives:


x = 15


The width of the rectangle is 15 cm.


From this you can determine the length.