The length of the prism is 32 cm, the width is 24 cm, the height is 44 cm, and the length of the diagonal of the base 40 cm. Find the length of the diagonal of the rectangular prism. Round the answer to the nearest tenth.
Let $x$ be the length of the diagonal.
Let $a$, $b$, and $c$ be the length, width, and height, respectively, of the rectangular prism. We have the equations $a=32$, $b=24$, $c=44$, $a^2+b^2=40^2=1600$, and $a^2+b^2+c^2=x^2$. Since $c$ is the longest side length, C is the answer. The length of the diagonal of the rectangular prism is $\boxed{55.2}$.
To find the length of the diagonal of the rectangular prism, we can use the Pythagorean theorem.
Let's denote the length of the diagonal of the rectangular prism as "d."
According to the given information, the length of the base diagonal is 40 cm. Let's denote it as "d₁."
Using the Pythagorean theorem, we have:
d₁² = length² + width²
40² = 32² + 24²
1600 = 1024 + 576
1600 = 1600
Therefore, we can conclude that the given information is consistent.
Now, let's use the Pythagorean theorem to find the length of the diagonal of the prism.
d² = d₁² + height²
d² = 40² + 44²
d² = 1600 + 1936
d² = 3536
Finally, we can calculate the value of "d" by taking the square root of 3536:
d ≈ √3536 ≈ 59.4 cm
Therefore, the length of the diagonal of the rectangular prism is approximately 59.4 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 a right triangle with the length and width of the base. We are given the length and the width of the base, but we need to find the length of the diagonal of the rectangular prism.
Let's call the length of the diagonal of the rectangular prism "d." According to the problem, we are given the length (32 cm), width (24 cm), and the length of the diagonal of the base (40 cm). We need to find the length of the diagonal of the rectangular prism (d).
To find d, we can use the Pythagorean theorem.
Using the Pythagorean theorem, we have:
d^2 = length^2 + width^2
Substituting the given values, we get:
d^2 = (32 cm)^2 + (24 cm)^2
d^2 = 1024 cm^2 + 576 cm^2
d^2 = 1600 cm^2
Taking the square root of both sides to solve for d, we get:
d = √(1600 cm^2)
d ≈ 40 cm
Therefore, the length of the diagonal of the rectangular prism is approximately 40 cm.