To determine the distance between two opposite corners of the floor, we can use the Pythagorean theorem. The Pythagorean theorem is commonly used to find the length of the hypotenuse in a right triangle, given the lengths of the other two sides.
Here's a step-by-step guide to solving this problem:
1. Identify the dimensions of the floor:
- Length ([tex]\(a\)[/tex]): 3 meters
- Width ([tex]\(b\)[/tex]): 8 meters
2. Set up the Pythagorean theorem:
The Pythagorean theorem states that [tex]\(a^2 + b^2 = c^2\)[/tex], where:
- [tex]\(a\)[/tex] and [tex]\(b\)[/tex] are the lengths of the two legs of the right triangle,
- [tex]\(c\)[/tex] is the length of the hypotenuse, the distance between the two opposite corners.
3. Substitute the given values into the theorem:
[tex]\[
3^2 + 8^2 = c^2
\][/tex]
4. Calculate the squares of the lengths:
[tex]\[
3^2 = 9
\][/tex]
[tex]\[
8^2 = 64
\][/tex]
5. Add these squared values:
[tex]\[
9 + 64 = 73
\][/tex]
6. Take the square root of the sum to find [tex]\(c\)[/tex]:
[tex]\[
c = \sqrt{73}
\][/tex]
7. Using a calculator to find the square root:
[tex]\[
\sqrt{73} \approx 8.54400374531753
\][/tex]
8. Round the result to the nearest tenth:
[tex]\[
8.54400374531753 \approx 8.5
\][/tex]
So, the distance between the two opposite corners of the floor, rounded to the nearest tenth, is 8.5 meters.
