In rectangular parallelepiped ABCDA1B1C1D1 it is known that BD1 = 27 BB1 = 2√26 AB = 24 Find the length AD.
| September 21, 2021 | education
At the base of a rectangular parallelepiped is a rectangle. Let us draw the diagonal BD at the base and determine its length according to the Pythagorean theorem from the right-angled triangle BD1D.
DD1 = BB1 = 2 * √26 cm, then:
BD ^ 2 = BD1 ^ 2 – DD1 ^ 2 = 27 ^ 2 – (2 * √26) ^ 2 = 729 – 104 = 625.
ВD = 25 cm.
From the right-angled triangle ABD we determine the length of the leg AD.
AD ^ 2 = BD ^ 2 – AB ^ 2 = 25 ^ 2 – 24 ^ 2 = 625 – 576 = 49.
AD = 7 cm.
Second way.
The square of the diagonal of a rectangular parallelepiped is equal to the sum of the squares of the lengths of its sides.
BD1 ^ 2 = AB ^ 2 + BB1 ^ 2 + AD ^ 2.
AD ^ 2 = BD1 ^ 2 – AB ^ 2 – BB1 ^ 2 = 729 – 576 – 104 = 49.
AD = 7 cm.
Answer: The length of the BP side is 7 cm.
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