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.

side line is 6m
bottom line is 7m

(1 point)
Responses

13 m
13 m

5.10 m
5.10 m

9.22 m
9.22 m

9 m
9 m

1 answer

To determine the length of the fence needed to divide Mia's rectangular garden into two triangular areas, we can think of the garden as a rectangle with a width of 6 meters and a length of 7 meters. To divide it into two triangles, the fence would have to run from one corner of the rectangle to the opposite corner (diagonal).

The length of the diagonal can be calculated using the Pythagorean theorem:

\[ d = \sqrt{a^2 + b^2} \]

Where:

  • \(a\) is the width (6 m)
  • \(b\) is the length (7 m)

Plugging in the values:

\[ d = \sqrt{6^2 + 7^2} \] \[ d = \sqrt{36 + 49} \] \[ d = \sqrt{85} \] \[ d \approx 9.22 \text{ m} \]

Thus, the length of the fence Mia will need is approximately 9.22 m.

The correct response is: 9.22 m