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.

3 answers

To find the length of the diagonal of the rectangular prism, segment BE , we can use the Pythagorean theorem.

First, let's find the length of segment HE using the Pythagorean theorem in triangle BEH :
HE² = BH² - BE²
HE² = 40² - 24²
HE² = 1600 - 576
HE² = 1024
HE = √1024
HE = 32 cm

Next, let's find the length of segment BE using the Pythagorean theorem in triangle BHE :
BE² = BH² + HE²
BE² = 40² + 32²
BE² = 1600 + 1024
BE² = 2624
BE = √2624
BE ≈ 51.2 cm

Therefore, the length of the diagonal of the rectangular prism, segment BE , is approximately 51.2 cm when rounded to the nearest tenth.
are you sure
Let's go back and double-check our calculations.

We found that HE = 32 cm, which we know is correct.

Next, let's recalculate the length of segment BE using the Pythagorean theorem in triangle BHE:

BE² = BH² + HE²
BE² = 40² + 32²
BE² = 1600 + 1024
BE² = 2624
BE = √2624
BE ≈ 51.2 cm

After recalculating, we find that the length of the diagonal of the rectangular prism, segment BE, is indeed approximately 51.2 cm when rounded to the nearest tenth.