# 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.**

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The ratio of the perimeters is equal to the scale factor. If rectangle #1 has sides L and W, then the perimeter is 2*L1 + 2*W1 = 2*(L1 + W1). If rectangle # 2 is similar to #1 and sides are scaled by a factor S, so that L2 = S*L1 and W2 = S*W1, the perimeter of rectangle #2 is 2*(L2 + W2)= 2*(S*L1 + S*W1) = S*2*(L1 + W1) = S*(perimeter of rectangle…

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