What is the length of the longest rod that can lie flat in rectangular box which is 2m long and 11/2 wide?
The longest rod that can lie flat in the rectangular box must have a length equal to the diagonal of the box. Using the Pythagorean theorem, we have:
length^2 = 2^2 + (11/2)^2
length^2 = 4 + 30.25
length^2 = 34.25
length = √34.25
Therefore, the length of the longest rod that can lie flat in the rectangular box is approximately 5.851 meters.
To find the length of the longest rod that can lie flat in the rectangular box, you need to determine the diagonal length of the box. You can use the Pythagorean theorem to calculate the diagonal length of the rectangular box. The Pythagorean theorem states that in a right-angled triangle, the square of the length of the hypotenuse (diagonal) is equal to the sum of the squares of the lengths of the other two sides.
In this case, the length of the box is given as 2m, and the width is 11/2 meters. Let's calculate the length of the longest rod step-by-step.
Step 1: Convert the width to a decimal.
The width of the box is given as 11/2. To convert this to a decimal, divide the numerator (11) by the denominator (2):
11 ÷ 2 = 5.5
Therefore, the width of the box is 5.5 meters.
Step 2: Calculate the diagonal length using the Pythagorean theorem.
Let's assume the length of the diagonal to be 'd.' We can set up the following equation using the Pythagorean theorem:
d^2 = (2^2) + (5.5^2)
Simplifying it further:
d^2 = 4 + 30.25
d^2 = 34.25
Taking the square root of both sides:
d ≈ √34.25
d ≈ 5.85
Therefore, the diagonal length of the rectangular box is approximately 5.85 meters.
So, the length of the longest rod that can lie flat in the rectangular box is 5.85 meters.