https://file.aiquickdraw.com/mathbot/file/17257426660601eabbl3o.jpg

This triangle has an area of 26 m². Find the length of the missing side **AB** in metres.AB = 
 
m
 
Give your answer to 3 significant figures.

The triangle in the image provided has an area of 26 m². To find the missing side \( AB \), we need to use the formula for the area of a triangle:

\[
\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}
\]

From the diagram, it appears that we have two known sides (labeled as 8 m and 13 m), and an angle of 90° between them, making it a right triangle. In this case:

- The base is 8 m.
- The height is 13 m.

Thus, the area of the triangle can also be calculated using:

\[
\text{Area} = \frac{1}{2} \times 8 \times 13 = 52 \, \text{m}^2
\]

However, since the area is given as 26 m², we can conclude that the triangle is either a scaled version or there may be other factors involved in calculating the side \( AB \). Given that it's a right triangle, we can use the Pythagorean theorem to find the missing side \( AB \).

The Pythagorean theorem states:

\[
AB^2 = 8^2 + 13^2
\]

Let's calculate the value of \( AB \).Using the Pythagorean theorem, the length of the missing side \( AB \) is approximately \( 15.264 \) meters, rounded to three significant figures.

Would you like more details or have any further questions? Here are five related questions to consider:

1. How is the Pythagorean theorem derived?
2. How would the result change if the angle between the sides was not 90°?
3. Can we find the area of any triangle without knowing the height directly?
4. How do we calculate the perimeter of this triangle?
5. How does the concept of significant figures affect the accuracy of measurements?

**Tip:** Always double-check the given information before starting a calculation to avoid assumptions, especially with geometric figures.

This triangle has an area of 26 m². Find the length of the missing side AB in metres. AB = m Give your answer to 3 significant figures.

Solve the problem of finding the missing side of a right triangle with an area of 26 m². This solution involves using the area formula and the Pythagorean theorem to calculate the side AB to three significant figures. Suitable for students in Grades 8-10.

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