4. Find the diagonal of a rectangular prism box that has measures of 3 x 4 x 10 cm. Round to nearest tenth.
To find the diagonal of a rectangular prism, we can use the Pythagorean theorem. The diagonal is the hypotenuse of a right triangle formed by the three edges of the rectangular prism.
We can label the three edges as follows:
a = 3 cm
b = 4 cm
c = 10 cm
Using the Pythagorean theorem, we have:
diagonal^2 = a^2 + b^2 + c^2
Substituting the given values, we get:
diagonal^2 = 3^2 + 4^2 + 10^2
= 9 + 16 + 100
= 125
Taking the square root of both sides, we find:
diagonal ≈ √125
≈ 11.2 cm
Therefore, the diagonal of the rectangular prism is approximately 11.2 cm (rounded to the nearest tenth).