E
D
F
diagonal
G
height
H
O
length
C
width
B
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 segment BR is 40 cm F the length of the diagonal of the rectangular prism segment BE Round the answer to the nearest tenth
(1 point)
59.5 cm
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The length of the diagonal of the rectangular prism segment BE can be found by using the Pythagorean theorem.
We know that the length BR is 40 cm, the width BC is 24 cm, and the height BO is 44 cm.
Using the Pythagorean theorem, we can find the length of the diagonal BE:
BE^2 = BR^2 + BC^2 + BO^2
BE^2 = 40^2 + 24^2 + 44^2
BE^2 = 1600 + 576 + 1936
BE^2 = 4112
BE ≈ √4112
BE ≈ 64.1 cm
Therefore, the length of the diagonal of the rectangular prism segment BE is approximately 64.1 cm.
To find the length of the diagonal of the rectangular prism segment BE, we can use the Pythagorean theorem. The Pythagorean theorem states that the square of the length of the hypotenuse of a right triangle is equal to the sum of the squares of the lengths of the other two sides.
In this case, segment BE represents the hypotenuse of a right triangle, with segments BR and RE as the other two sides.
We have the length of segment BR (the diagonal of the base segment BR) as 40 cm. We also know the width and the height of the rectangular prism, which are 24 cm and 44 cm respectively.
To find the length of segment RE, we can use the Pythagorean theorem. Let's calculate it step by step:
1. Calculate the square of the length of segment BR:
BR² = 40² = 1600 cm²
2. Calculate the square of the length of the width of the prism segment BE:
Width² = 24² = 576 cm²
3. Calculate the square of the length of the height of the prism segment BE:
Height² = 44² = 1936 cm²
4. Calculate the sum of the squares of the width and height:
Sum of squares = Width² + Height² = 576 cm² + 1936 cm² = 2512 cm²
5. Subtract the square of the length of segment BR from the sum:
Difference = Sum of squares - BR² = 2512 cm² - 1600 cm² = 912 cm²
6. Take the square root of the difference to find the length of segment RE:
RE = √Difference = √912 cm² ≈ 30.2 cm
Therefore, the length of segment BE (the diagonal of the rectangular prism segment BE) is approximately 30.2 cm when rounded to the nearest tenth.
To find the length of the diagonal of the rectangular prism segment BE, we can use the Pythagorean theorem.
1. First, let's find the length of the segment BR using the given information. We can consider BR as the hypotenuse of a right triangle formed by the dimensions of the base.
Using the Pythagorean theorem:
BR^2 = length^2 + width^2
BR^2 = 32^2 + 24^2
BR^2 = 1024 + 576
BR^2 = 1600
Taking the square root of both sides:
BR ≈ √1600
BR ≈ 40 cm
2. Now, let's find the length of the segment BE, which is the diagonal of the rectangular prism.
Using the Pythagorean theorem again, but this time considering BE as the hypotenuse of a right triangle formed by the diagonal (BR) and the height (h) of the prism:
BE^2 = BR^2 + h^2
BE^2 = 40^2 + 44^2
BE^2 = 1600 + 1936
BE^2 = 3536
Taking the square root of both sides:
BE ≈ √3536
BE ≈ 59.5 cm (rounded to the nearest tenth)
Therefore, the length of the diagonal of the rectangular prism segment BE is approximately 59.5 cm.