Question

The length of the rectangle is 8cm longer than the width.

Answer 1

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