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.
a 46.6 cm
b 59.5 cm
c 54.4 cm
d 51.2 cm
We can use the Pythagorean theorem to find the length of the diagonal of the rectangular prism.
Let's consider segment BH as the hypotenuse of a right triangle formed by the length, width, and diagonal of the base.
By the Pythagorean theorem, we have:
$(BH)^2 = (32)^2 + (24)^2$
Simplifying, we get:
$(BH)^2 = 1024 + 576$
$(BH)^2 = 1600$
Taking the square root of both sides, we find:
$BH = 40$
Now, let's consider segment BE as the hypotenuse of a right triangle formed by the length, width, and diagonal of the prism.
Again, by the Pythagorean theorem, we have:
$(BE)^2 = (40)^2 + (44)^2$
$(BE)^2 = 1600 + 1936$
$(BE)^2 = 3536$
Taking the square root of both sides, we find:
$BE = \sqrt{3536} \approx 59.5$
Therefore, the length of the diagonal of the rectangular prism, segment BE, is approximately 59.5 cm.
The correct answer is b) 59.5 cm.