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 rectangle prism, segment BE. Round to the nearest tenth
To find the length of the diagonal segment BE, we can use the Pythagorean Theorem in the right triangle BHE.
Given:
Length (l) = 32 cm
Width (w) = 24 cm
Height (h) = 44 cm
Diagonal of the base (BH) = 40 cm
We can split the diagonal BH into two segments:
BH = BE + EH
EH is the height of the right triangle BHE, which is the height of the prism:
EH = h = 44 cm
We can find the base of the right triangle BHE using the Pythagorean Theorem:
l^2 + w^2 = BE^2
32^2 + 24^2 = BE^2
1024 + 576 = BE^2
1600 = BE^2
BE = √1600
BE = 40 cm
Now, we can find the length of the diagonal segment BE:
BH = BE + EH
40 cm = 40 cm + 44 cm
40 cm = 84 cm
Therefore, the length of the diagonal segment BE is 84 cm.