What is the length and width of a rectangle with a perimeter of 135 and a scale factor of 8 to 1?

Let w equal the width and l equal the length of the rectangle. This means that 2w+2l=135 and since the rectangle has a scale factor of 8:1, that w/l=8. We now have a system of equations. Solve the second equation for w and find that w=8l. Substitute this into the first equation and find that 2(8l)+2l=135, which simplifies to 18l=135. Solve for l to get l=7.5 units. Plug this into either of the original equations to find that w=60 units. The dimensions of the rectangle are 60 by 7.5 units.