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.

6m, 7m, __m

(1 point)
Responses

13 m
13 m

9 m
9 m

5.10 m
5.10 m

9.22 m

Answer 1

To find the length of the fence that Mia needs, we can use the Pythagorean theorem. The garden is being divided into two triangular areas, which likely means that we have a right triangle based on the given dimensions.

Let's assume Mia's garden is a right triangle with legs measuring 6m and 7m.

According to the Pythagorean theorem:

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

Where:
- \(c\) is the hypotenuse (the length of the fence),
- \(a\) and \(b\) are the legs of the right triangle.

Substituting the values:

\[
c = \sqrt{6^2 + 7^2}
\]

Calculating the squares:

\[
c = \sqrt{36 + 49}
\]
\[
c = \sqrt{85}
\]

Now, compute the square root:

\[
c \approx 9.22 \text{ m}
\]

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

So the correct response is:

**9.22 m**