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