The length of a rectangle is 6 cm longer than the width. if the length is increased by 9 cm and the width by 5 cm, the perimeter will be 160 cm. find the dimensions of the original rectangle.

We're going to make the equation in terms of w, since the length is 6 cm longer. We are going to have the equation equal 160 cm, since that is the perimeter.
2(w+5) + 2(w+ 6 + 9) = 160
We can add in the parenthesis.
2(w+5) + 2(w+15)
Distribute.
2w+10+2w+30=160
Add like terms.
4w+ 40 = 160
4w=120
w=30
The width is 30 cm and the length is 36 cm.
Let's check by making the rectangle again.
2(45) + 2(35)=160
90+ 70 = 160