Question

use the image to answer the question.
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)

Explanation:

Step1: Apply Pythagorean theorem

In right - triangle \(BEH\), if the length of the base diagonal \(BH = 40\) cm and the height \(EH=44\) cm. According to the Pythagorean theorem \(a^{2}+b^{2}=c^{2}\), where \(a = BH\), \(b = EH\), and \(c = BE\).
So, \(BE^{2}=BH^{2}+EH^{2}\)

Step2: Substitute values

Substitute \(BH = 40\) and \(EH = 44\) into the formula:
\(BE^{2}=40^{2}+44^{2}\)
\(BE^{2}=1600 + 1936\)
\(BE^{2}=3536\)

Step3: Solve for \(BE\)

Take the square root of both sides: \(BE=\sqrt{3536}\approx59.5\)

Answer:

\(59.5\) cm