what is the length of the diagonal for the given rectangular prism to the nearest whole unit
Length: 8 cm
Width: 3 cm
Height: 7 cm
A. 10 cm
B. 11 cm
C. 6 cm
D.13 cm
please help I cant figure it out
B. 11 cm
the length is √(8^2 + 3^2 + 7^2) = √122
To find the length of the diagonal in the rectangular prism, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right-angled triangle, the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides.
Let's label the length, width, and height of the rectangular prism as a, b, and c respectively.
In this case:
Length (a) = 8 cm
Width (b) = 3 cm
Height (c) = 7 cm
To find the diagonal, we can create a right-angled triangle using the length, width, and height. The diagonal will be the hypotenuse of this triangle.
The formula to find the diagonal (D) is:
D² = a² + b² + c²
Substituting the given values, we have:
D² = 8² + 3² + 7²
D² = 64 + 9 + 49
D² = 122
To find the length of the diagonal to the nearest whole unit, we need to find the square root of 122: √122 ≈ 11.0
Therefore, the length of the diagonal to the nearest whole unit is 11 cm.
So, the answer is B. 11 cm.
To find the length of the diagonal of a rectangular prism, you can use the Pythagorean theorem, which states that the sum of the squares of the lengths of the two shorter sides of a right triangle is equal to the square of the length of the hypotenuse (the longest side).
In this case, the length (L) of the rectangular prism is 8 cm, the width (W) is 3 cm, and the height (H) is 7 cm. To find the length of the diagonal, we need to find the length of the hypotenuse of the right triangle formed by the height (H), width (W), and diagonal (D).
Using the Pythagorean theorem, we can write the equation as:
D² = H² + W²
Substituting the given values, we have:
D² = 7² + 3²
D² = 49 + 9
D² = 58
To find the length of the diagonal (D), we need to take the square root of both sides:
D = √58
Now, to find the nearest whole unit, you need to round the value of √58 to the nearest whole number. Evaluating this using a calculator, we get:
D ≈ 7.62
The nearest whole unit is 8 cm.
Therefore, the correct answer is:
A. 10 cm