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 40 cm. Find the length of the diagonal of the rectangular prism. Round the answer to the nearest tenth.
a.46.6 cm
b.54.4 cm
c.59.5 cm
d.51.2 cm
To find the length of the diagonal of the rectangular prism, we can use the Pythagorean theorem.
The diagonal of the base forms a right triangle with the length and width of the prism. Let's call the length l and the width w.
Using the Pythagorean theorem, we have:
l^2 + w^2 = (40 cm)^2
We know that l = 32 cm and w = 24 cm, so substituting those values in, we get:
(32 cm)^2 + (24 cm)^2 = (40 cm)^2
1024 cm^2 + 576 cm^2 = 1600 cm^2
Next, we can find the length of the diagonal of the rectangular prism using the Pythagorean theorem.
Let's call the length of the diagonal d. We have:
d^2 = (32 cm)^2 + (24 cm)^2 + (44 cm)^2
Substituting the values, we get:
d^2 = 1024 cm^2 + 576 cm^2 + 1936 cm^2
d^2 = 3536 cm^2
Taking the square root of both sides, we get:
d = √(3536 cm^2)
Using a calculator, we find that:
d ≈ 59.5 cm
Therefore, the answer is c. 59.5 cm.