Question

Диагонали граней прямоугольного параллелепипеда равны 7см, 8см, 9 см. Найдите диагональ параллелепипеда

Answer 1

Пусть a,b,c- три измерения параллелепипеда,тогда по теореме Пифагора: a^2+b^2=49;

a^2+c^2=64;

b^2+c^2=81.

Сложив эти три равенства(как в системе),получим:

2a^2+2b^2+2c^2=49+64+81=194;

2( a^2+b^2+c^2)=194;

  a^2+b^2+c^2 =87.

Так как d^2= a^2+b^2+c^2, то d=sqrt(87)=9.33 

 

Answer 2

Calculating the Diagonal of a Rectangular Parallelepiped

The question states that the diagonals of the faces of the rectangular parallelepiped are 7 cm, 8 cm, and 9 cm.

To find the diagonal of the entire parallelepiped, we can use the Pythagorean theorem. The Pythagorean theorem states that for any right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

We know that the lengths of two edges of the parallelepiped are 8 cm and 9 cm. Using the Pythagorean theorem:

`a^2 + b^2 = c^2`

Where `a` and `b` are the two known edge lengths, and `c` is the diagonal we want to find. Plugging in the values:

`8^2 + 9^2 = c^2` `64 + 81 = c^2` `145 = c^2` `c = √145` `c = 12`

Therefore, the diagonal of the entire parallelepiped is 12 cm.