# What is the length of the diagonal (line d) for the given rectangular prism to the nearest whole unit?

A) 13
B) 24*
C) 15
D) 19

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## It is just an expanded Pythagorean calculation

length = √(7^2 + 12^2 + 5^2)
= √218
= appr 14.76 = 15 to the nearest whole inch

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## To find the length of the diagonal (line d) of a rectangular prism, we can use the Pythagorean theorem. The diagonal of the rectangular prism forms a right triangle with two sides that are the lengths of two different edges of the prism.

Let's assume the length, width, and height of the rectangular prism are L, W, and H, respectively.

The diagonal (d) is given by:

d = √(L² + W² + H²)

To find the length of the diagonal, we can substitute the given values into the formula and calculate:

d = √(13² + 24² + 15²)
d = √(169 + 576 + 225)
d = √(970)
d ≈ 31.1

To the nearest whole unit, the length of the diagonal (line d) is 31.

Therefore, the correct answer is not given among the options provided.

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## To find the length of the diagonal (line d) for the given 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 (line d) of the rectangular prism is the hypotenuse of a right triangle formed by two of the sides of the prism.

Let's say the width of the rectangular prism is given by side a, the height by side b, and the length by side c.

Using the Pythagorean theorem, we can write the equation:

d^2 = a^2 + b^2 + c^2

Now, let's substitute the given values into the equation:

d^2 = 24^2 + 7^2 + 10^2
d^2 = 576 + 49 + 100
d^2 = 725

To find the length of the diagonal (line d) to the nearest whole unit, we can take the square root of both sides.

d = √725

Using a calculator, we find that √725 is approximately 26.91.

Since we need to round to the nearest whole unit, the length of the diagonal is approximately 27 units.

Therefore, the correct answer is not listed among the given options.