What is the length of the diagonal for the given rectangular prism to the nearest whole unit?
A rectangular prism is shown. A bold yellow line extends from the upper rear vertex to the lower front right vertex. To the right of the prism the text 'Length equals 6 centimeters', 'Width equals 5 centimeters', and 'Height equals 9 centimeters' is displayed.
A. 8 cm
B. 10 cm
C. 11 cm
D. 12 cm
To find the length of the diagonal of the rectangular prism, we can use the Pythagorean theorem. The diagonal is the hypotenuse of a right triangle whose legs are the length, width, and height of the prism.
Using the Pythagorean theorem, we have:
diagonal^2 = length^2 + width^2 + height^2
diagonal^2 = 6^2 + 5^2 + 9^2
diagonal^2 = 36 + 25 + 81
diagonal^2 = 142
diagonal ≈ 11.9
Rounding to the nearest whole unit, the length of the diagonal is 12 cm.
Therefore, the answer is D. 12 cm.
To find the length of the diagonal of a rectangular prism, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
In this case, the diagonal of the rectangular prism forms the hypotenuse of a right triangle. The length, width, and height of the rectangular prism are given, so we can use these values to find the length of the diagonal.
First, let's find the length of the hypotenuse using the Pythagorean theorem.
Length of the hypotenuse = √(Length^2 + Width^2 + Height^2)
= √(6^2 + 5^2 + 9^2)
= √(36 + 25 + 81)
= √142
≈ 11.92 cm
Since we want the answer to the nearest whole unit, the length of the diagonal of the rectangular prism is approximately 12 cm.
Therefore, the correct answer is D. 12 cm.
To find the length of the diagonal of a rectangular prism, we can use the Pythagorean theorem. The Pythagorean theorem states that the square of the length of the hypotenuse (diagonal) of a right triangle is equal to the sum of the squares of the other two sides.
In this case, the diagonal is the hypotenuse of a right triangle, while the length, width, and height of the rectangular prism are the other two sides.
Using the given dimensions:
Length = 6 cm
Width = 5 cm
Height = 9 cm
To find the length of the diagonal, we can use the formula:
Diagonal^2 = Length^2 + Width^2 + Height^2
Substituting the given values:
Diagonal^2 = 6^2 + 5^2 + 9^2
Diagonal^2 = 36 + 25 + 81
Diagonal^2 = 142
We need to find the square root of 142 to get the length of the diagonal.
√142 ≈ 11.92
Rounding this to the nearest whole unit, the length of the diagonal is 12 cm.
Therefore, the correct answer is D. 12 cm.