The length of the rectangle is 8cm longer than the width. if the length of the original rectangle is increased by 6cm and the width is increased by 3cm the perimeter is 76cm. what is the length of the original rectangle?

The length of the rectangle is 8cm longer than the width.
l=w+8
If the length of the original rectangle is increased by 6cm and the width is increased by 3cm the perimeter is 76cm.
p=76=((l+6)+(w+3))*2=(l+6+w+3)*2=(l+w+9)*2

to solve this substitute l=w+8 into the p= equation:
p=76=((w+8)+w+9)*2=
76=(2w+17)*2
76=4w+34
42=4w
10.5=w

l=w+8=10.5+8=18.5