Plots of land between two roads are laid out according to the boundaries shown. The boundaries between the two roads are parallel. What is the length of Plot 3 along Cheshire Road?

Answer 1

To find the length of Plot 3 along Cheshire Road, we need to add up the lengths of each segment.

First, we know that the lengths of the plots along Cheshire Road are in the ratio 2:3:4. Let's call the length of Plot 3 along Cheshire Road as $x$. The length of Plot 2 along Cheshire Road can be represented as $2x$ because it is twice the length of Plot 3 along Cheshire Road. The length of Plot 1 along Cheshire Road can be represented as $3x$ because it is three times the length of Plot 3 along Cheshire Road.

Adding up the lengths of the segments, we have:
$3x + 2x + x = 6x$

Thus, the total length of the segments along Cheshire Road is $6x$. Therefore, the length of Plot 3 along Cheshire Road is $\boxed{\frac{1}{6}}$ the total length of the segments along Cheshire Road.