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 BH, is 40 cm. Find the length of the diagonal of the rectangular prism, segment BE. Round the answer to the nearest tenth.
(1 point)
46.6 cm
O 54.4 cm
O 51.2 cm
O 59.5 cm
To find the length of the diagonal of the rectangular prism, segment BE, we can use the Pythagorean theorem.
Segment BE is the hypotenuse of a right triangle with sides BH and HE.
Using the Pythagorean theorem, we have:
BE^2 = BH^2 + HE^2
We already know that BH is 40 cm. To find HE, we can use the length and width of the prism.
HE is the height of the triangle, so HE = 44 cm.
Now we can substitute these values into the equation:
BE^2 = 40^2 + 44^2
BE^2 = 1600 + 1936
BE^2 = 3536
Taking the square root of both sides, we find:
BE ≈ √3536
BE ≈ 59.5 cm
Therefore, the length of the diagonal of the rectangular prism, segment BE, is approximately 59.5 cm.
The answer is O 59.5 cm.
To find the length of the diagonal of the rectangular prism, segment BE, we can use the Pythagorean theorem.
The diagonal of the prism, segment BE, is the hypotenuse of a right triangle formed by the length, width, and height of the prism.
By applying the Pythagorean theorem, we have:
BE² = BH² + HE²
BE is the length of the diagonal of the rectangular prism.
BH = 40 cm (length of diagonal of the base)
HE = height of the prism = 44 cm
Substituting the values, we get:
BE² = 40² + 44²
BE² = 1600 + 1936
BE² = 3536
Taking the square root of both sides, we get:
BE ≈ √3536
BE ≈ 59.4 cm
Therefore, the length of the diagonal of the rectangular prism, segment BE, is approximately 59.4 cm.
So, the correct answer is:
O 59.5 cm.
To find the length of the diagonal of the rectangular prism, segment BE, we can use the Pythagorean theorem.
First, let's find the length of segment BH in the base of the prism. We can use the Pythagorean theorem to do this.
The formula for the Pythagorean theorem is:
c² = a² + b²
In this case, a = 32 cm and b = 24 cm (the length and width of the base). Let's substitute these values into the formula:
BH² = 32² + 24²
BH² = 1024 + 576
BH² = 1600
To find the length of segment BE, which is the diagonal of the rectangular prism, we can use the Pythagorean theorem again.
In this case, a = BH = 40 cm (the length of segment BH from the given information) and b = the height of the prism = 44 cm. Let's substitute these values into the formula:
BE² = 40² + 44²
BE² = 1600 + 1936
BE² = 3536
Now, to find BE, we need to take the square root of both sides of the equation:
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. So the correct answer is O 59.5 cm.