Question

The floor of a storage unit is 7 feet long and 6 feet wide. What is the distance between two opposite corners of the floor? If necessary, round to the nearest tenth.

Answer 1

To find the distance between two opposite corners of a 7 feet by 6 feet floor, use the Pythagorean Theorem. The diagonal, which is the hypotenuse in this right triangle, is the square root of the sum of the squares of the lengths and widths. It calculates to approximately 9.2 feet.

Step-by-step explanation:

The question asks for the distance between two opposite corners of a storage unit floor that is 7 feet long and 6 feet wide. To find this distance, also known as the diagonal, we use the Pythagorean Theorem, which applies to right-angled triangles. This theorem states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b).

We can set the length and width as the two sides of a right triangle and the diagonal as the hypotenuse. Using the lengths provided:

• Length (a) = 7 feet
• Width (b) = 6 feet

According to the Pythagorean Theorem, we calculate the hypotenuse (c) as follows:

c² = a² + b²

c² = 7² + 6²

c² = 49 + 36

c² = 85

To find c, we take the square root of 85:

c = √85 ≈ 9.2 feet

Therefore, the distance between two opposite corners of the storage unit floor is approximately 9.2 feet. If needed, this value can be rounded to the nearest tenth as specified in the question.

Answer 2

`\text{Find the distance from one corner to the other}\\\\\text{In this question, we would use the Pythagorean theorem to find the length}\\\text{between corners}\\\\\text{Pythagorean theorem:}\\\\a^2+b^2=c^2\\\\\text{We are trying to find c}\\\\\text{Plug in and solve:}\\\\7^2+6^2=c^2\\\\49+36=c^2\\\\85=c^2\\\\\text{Square root}\\\\√(85)=√(c^2)\\\\√(85)=c\\\\\text{In decimal form, it's: 9.219544}\\\\\text{Round to the nearest tenths place}\\\\\boxed{9.2\,\, feet}`