The perimeter of a rectangle is 40 cm. the length is 12cm longer than the width. find the dimensions.

"The length is 12 cm longer than the width" means

Length = Width + 12
L = W+12

The perimeter of any rectangle is found by this formula
P = 2*(L+W)

Replace P with 40 since we know the perimeter is 40 cm

P = 2*(L+W)
40 = 2*(L+W)

and then replace L with W+12 (see above) to get

40 = 2*(L+W)
40 = 2*(W+12+W)

now solve for W, ie isolate it

40 = 2*(W+12+W)
40 = 2*(2W+12)
40 = 4W+24
4W+24 = 40
4W+24-24 = 40-24
4W = 16
4W/4 = 16/4
W = 4

Since the width is 4, we can use this to find the length L
W = 4
L = W+12
L = 4+12 ... replace W with 4
L = 16

In summary, we have
W = 4
L = 16
So this rectangle is 16 cm by 4 cm