The floor of a storage unit is 3 meters long and 8 meters wide. What is the distance between two opposite corners of the floor? If necessary, round to the nearest tenth.

Use the Pythagorean theorem to solve the problem.



Answer :

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.