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
To find the length of the diagonal of the rectangular prism, segment BE, we can use the Pythagorean theorem.
Let's first find the length of segment EH. We can do this by using the Pythagorean theorem with the given dimensions of the prism's base. We have BH = 40 cm, and BH represents the hypotenuse of right triangle BEH. The other two sides are the length and the width of the prism's base.
Using the Pythagorean theorem, we can write:
BE^2 = BH^2 - EH^2.
Since the length of the prism is 32 cm and the width is 24 cm, the length and the width of the base form a right-angle triangle with sides 32 cm and 24 cm.
Let's call the length of segment EH as x.
Now we can substitute the values into the equation:
x^2 = 40^2 - 32^2 - 24^2.
Simplifying:
x^2 = 1600 - 1024 - 576.
x^2 = 0.
Since x^2 = 0, this means x = 0.
Therefore, the length of segment EH is 0 cm.
Now we can find the length of segment BE:
BE^2 = BH^2 - EH^2.
BE^2 = 40^2 - 0^2.
BE^2 = 1600.
Taking the square root of both sides:
BE ≈ √1600.
BE ≈ 40 cm.
Therefore, the length of diagonal segment BE is approximately 40 cm, rounded to the nearest tenth.