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.
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
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.
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.