A rectangular hall is 5 feet long and 4 feet wide. How long is a walkway along the diagonal?
2.8 inches
5.6 inches
6.4 inches
3.6 inches
To find the length of the walkway along the diagonal, we can use the Pythagorean theorem. The length of the walkway is the hypotenuse of a right triangle with sides measuring 4 feet and 5 feet.
Using the Pythagorean theorem:
a^2 + b^2 = c^2
where a and b are the lengths of the sides of the right triangle, and c is the length of the hypotenuse (the walkway).
Plugging in the values:
4^2 + 5^2 = c^2
16 + 25 = c^2
41 = c^2
Taking the square root of both sides to solve for c:
c = √41 ≈ 6.4 inches
Therefore, the length of the walkway along the diagonal is approximately 6.4 inches. Thus, the correct answer is 6.4 inches.
To find the length of the walkway along the diagonal, we can use the Pythagorean theorem. The theorem states that in a right triangle, the square of the length of the hypotenuse (in this case, the diagonal) is equal to the sum of the squares of the other two sides.
In this case, the length and width of the rectangular hall form the two sides of the right triangle, and the diagonal is the hypotenuse.
Let's calculate it step-by-step:
Step 1: Square the length: 5^2 = 25
Step 2: Square the width: 4^2 = 16
Step 3: Sum the squares of the length and width: 25 + 16 = 41
Step 4: Take the square root of the result: √41 ≈ 6.4
Therefore, the length of the walkway along the diagonal is approximately 6.4 inches.
So, the correct answer is: 6.4 inches.