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)
Responses
51.2 cm
51.2 cm
59.5 cm
59.5 cm
54.4 cm
54.4 cm
46.6 cm
46.6 cm
To find the length of diagonal BE, we can use the Pythagorean theorem on triangle BEH.
The length of BH is given as 40 cm, and we can use the formula for the diagonal of a rectangle, which states that the diagonal squared is equal to the sum of the lengths squared, to find the length of EH.
EH^2 = BH^2 - BH^2
EH^2 = 40^2 - 24^2
EH^2 = 1600 - 576
EH^2 = 1024
EH = √1024
EH = 32
Now, we can use the Pythagorean theorem on triangle BEH to find the length of BE.
BE^2 = EH^2 + BH^2
BE^2 = 32^2 + 40^2
BE^2 = 1024 + 1600
BE^2 = 2624
BE = √2624
BE ≈ 51.2 cm
Therefore, the length of diagonal BE is approximately 51.2 cm