Question 208615
Let l be the length and w be the width.  We know that perimeter is 48 so in equations this would be l + w =48 so that will be our first equation.  We also know that the length of is 12 cm longer than the width.  In equations this would be l = 12+w, which is our second equation. <br>

so our system is <br>

l + w = 48
l = 12 + w <br>

So since we have an expression for l we can use the substitution method and plug equation 2 into equation 1 and solve for width. <br>

l + w = 48
12 + w + w = 48
12 + 2w = 48
2w = 36
w = 18 cm <br>

so we know the width is 18 centimeters.  Now we plug that back into equation 2 and find the length. <br>

l = 12 + w
l = 12 + 18
l = 30 cm <br>

so we know that the width is 18 centimeters and the length is 30 centimeters and checking that does give us a perimeter of 48 centimeters so that checks.