To solve the problem, let's carefully analyze the given image and the task. The image shows a rectangle $ABCD$ with certain dimensions and additional points and segments marked. Here is the step-by-step solution:
Step 1: Understand the Dimensions
- The rectangle $ABCD$ has:
- Length $AB = 10 \, \text{cm}$.
- Width $AD = 8 \, \text{cm}$.
- Additional points and segments are marked:
- Point $E$ is on side $BC$, such that $BE = 8 \, \text{cm}$.
- Point $F$ is on side $AD$, such that $AF = 2 \, \text{cm}$.
- Segment $EF$ is drawn, connecting points $E$ and $F$.
Step 2: Determine Coordinates of Points
To simplify the problem, we can place the rectangle in a coordinate system:
- Let $A = (0, 8)$.
- Let $B = (10, 8)$.
- Let $C = (10, 0)$.
- Let $D = (0, 0)$.
Using these coordinates:
- Point $F$ is on $AD$, which is the vertical line segment from $(0, 8)$ to $(0, 0)$. Since $AF = 2 \, \text{cm}$, the coordinates of $F$ are:
$$
F = (0, 2).
$$
- Point $E$ is on $BC$, which is the horizontal line segment from $(10, 8)$ to $(10, 0)$. Since $BE = 8 \, \text{cm}$, the coordinates of $E$ are:
$$
E = (10, 0).
$$
Step 3: Calculate the Length of Segment $EF$
The length of segment $EF$ can be found using the distance formula between two points $(x_1, y_1)$ and $(x_2, y_2)$:
$$
\text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}.
$$
Here, the coordinates of $E$ are $(10, 0)$ and the coordinates of $F$ are $(0, 2)$. Substituting these into the distance formula:
$$
EF = \sqrt{(10 - 0)^2 + (0 - 2)^2} = \sqrt{10^2 + (-2)^2} = \sqrt{100 + 4} = \sqrt{104} = 2\sqrt{26}.
$$
Final Answer
The length of segment $EF$ is:
$$
\boxed{2\sqrt{26}}
$$
Parent Tip: Review the logic above to help your child master the concept of perimeter of irregular polygons worksheet.
