Question
Question
Sampson has a garden as shown below. He wants to build a fence from one corner of the garden to the other. How many meters of fencing does Sampson need? Round your answer to the nearest meter as necessary.
Rectangle with side lengths 20 m and 12 m. Diagonal line connecting bottom left corner to top right corner labeled fence.
fence length =
m
Sampson has a garden as shown below. He wants to build a fence from one corner of the garden to the other. How many meters of fencing does Sampson need? Round your answer to the nearest meter as necessary.
Rectangle with side lengths 20 m and 12 m. Diagonal line connecting bottom left corner to top right corner labeled fence.
fence length =
m
Answers
GPT-4o mini
To find the length of the fence that Sampson needs, we can calculate the length of the diagonal of the rectangle using the Pythagorean theorem.
For a rectangle with side lengths \(a = 20\) m and \(b = 12\) m, the length of the diagonal \(d\) can be calculated with the formula:
\[
d = \sqrt{a^2 + b^2}
\]
Substituting the values:
\[
d = \sqrt{20^2 + 12^2}
\]
\[
d = \sqrt{400 + 144}
\]
\[
d = \sqrt{544}
\]
\[
d \approx 23.32 \text{ m}
\]
Rounding to the nearest meter, Sampson needs approximately:
\[
\text{fence length} = 23 \text{ m}
\]
Thus, the length of the fence Sampson needs is **23 meters**.
For a rectangle with side lengths \(a = 20\) m and \(b = 12\) m, the length of the diagonal \(d\) can be calculated with the formula:
\[
d = \sqrt{a^2 + b^2}
\]
Substituting the values:
\[
d = \sqrt{20^2 + 12^2}
\]
\[
d = \sqrt{400 + 144}
\]
\[
d = \sqrt{544}
\]
\[
d \approx 23.32 \text{ m}
\]
Rounding to the nearest meter, Sampson needs approximately:
\[
\text{fence length} = 23 \text{ m}
\]
Thus, the length of the fence Sampson needs is **23 meters**.