In rectangular parallelepiped ABCDA1B1C1D1 it is known that BB1 = 9; A1B1 = 2
| September 16, 2021 | education
In rectangular parallelepiped ABCDA1B1C1D1 it is known that BB1 = 9; A1B1 = 2; A1D1 = 6. Find the length of the diagonal BD1.
Diagonal B1D1 divides the base into 2 identical right-angled triangles. In which A1B1 and A1D1 are legs. Let us find the diagonal В1D1 by the Pythagorean theorem.
B1D1 = √ ((2 cm) ² + (6 cm) ²) = √40 cm² = 6.3 cm.
The height of the box BB1, the diagonal of the upper base B1D1 and the diagonal of the box BD1 form a rectangular triangle in which BD1 is the hypotenuse.
Find the diagonal BD1 by the Pythagorean theorem.
BD1 = B1D1 = √ ((9 cm) ² + (6.3 cm) ²) = 11 cm.
Answer: The diagonal of BD1 is 11 cm.
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