The problem asks to estimate the length of side $KL$ in the given diagram.

1. Problem Description

The problem asks to estimate the length of side $KL$ in the given diagram.

2. Solution Steps

By observing the diagram, the coordinates of point $K$ appear to be approximately $(8, 2)$ and the coordinates of point $L$ appear to be approximately $(1, 9)$. Therefore, the length of $KL$ can be estimated using the distance formula:

$d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$

Where $(x_1, y_1) = (1, 9)$ and $(x_2, y_2) = (8, 2)$.

$KL = \sqrt{(8 - 1)^2 + (2 - 9)^2}$

$KL = \sqrt{(7)^2 + (-7)^2}$

$KL = \sqrt{49 + 49}$

$KL = \sqrt{98}$

$KL \approx 9.899$

The grid lines are 1 unit apart. By visually estimating, $KL$ seems to be close to

1

0.

Based on the image, $KM$ appears to be from $x=1$ to $x=8$, so $KM = 7$. $LM$ appears to be from $y=2$ to $y=9$, so $LM=7$. Then $KL = \sqrt{7^2 + 7^2} = \sqrt{49 + 49} = \sqrt{98} \approx 9.9$.

Therefore, rounding the answer to the nearest whole number, the estimated length of $KL$ is approximately 10 cm.

3. Final Answer

10