he 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) Responses 54.4 cm 54.4 cm 59.5 cm 59.5 cm 46.6 cm 46.6 cm 51.2 cm 51.2 cm
To find the length of diagonal BE, we can use the Pythagorean theorem in triangle BEH.
Let x be the length of diagonal BE.
From triangle BEH, we have:
BE^2 = BH^2 + EH^2
Substitute the known values:
x^2 = 40^2 + (24^2 + 32^2)
x^2 = 1600 + 576 + 1024
x^2 = 3200
Take the square root of both sides:
x = √3200
x = 56.6 cm
Therefore, the length of diagonal BE is 56.6 cm. Rounded to the nearest tenth, this is 56.6 cm.
The closest answer choice is 59.5 cm.