Question
Mia plans to build a fence to divide her rectangular garden into two triangular areas. Use the diagram to find the length of the fence she will need to divide the garden. Round your answer to the nearest hundredth.
The side of the rectangle is 6m
The bottom of the rectangle is 7m
The side of the rectangle is 6m
The bottom of the rectangle is 7m
Answers
GPT-4o mini
To divide a rectangular garden into two triangular areas using a fence, Mia can create a diagonal line from one corner of the rectangle to the opposite corner. The garden has dimensions of 6 m (height) and 7 m (width).
The length of the diagonal can be calculated using the Pythagorean theorem. The formula for the diagonal \( d \) of a rectangle is:
\[
d = \sqrt{(width^2 + height^2)}
\]
In Mia's case, the width is 7 m, and the height is 6 m.
Now, substitute the values into the formula:
\[
d = \sqrt{(7^2 + 6^2)}
\]
\[
d = \sqrt{(49 + 36)}
\]
\[
d = \sqrt{85}
\]
Calculating \( \sqrt{85} \):
\[
d \approx 9.219544
\]
Rounding this to the nearest hundredth, the length of the fence needed is:
\[
d \approx 9.22 \text{ m}
\]
Thus, Mia will need approximately **9.22 m** of fence to divide her garden.
The length of the diagonal can be calculated using the Pythagorean theorem. The formula for the diagonal \( d \) of a rectangle is:
\[
d = \sqrt{(width^2 + height^2)}
\]
In Mia's case, the width is 7 m, and the height is 6 m.
Now, substitute the values into the formula:
\[
d = \sqrt{(7^2 + 6^2)}
\]
\[
d = \sqrt{(49 + 36)}
\]
\[
d = \sqrt{85}
\]
Calculating \( \sqrt{85} \):
\[
d \approx 9.219544
\]
Rounding this to the nearest hundredth, the length of the fence needed is:
\[
d \approx 9.22 \text{ m}
\]
Thus, Mia will need approximately **9.22 m** of fence to divide her garden.