Question

Діагональ прямокутного паралелепіпеда дорівнює √38 см, діагональ бічних граней - √29 см і √34 см. Знайти сторони основ паралелепіпеда

Answer 1

Пошаговое объяснение:

диагональ параллелепипеда:d=√38 см

диагональ грани :d1=√29 см

диагональ грани : d2=√34 см

а=? ; b=?

по теореме Пифагора:

d1²=a²+c² ;(√29)²=a²+c² ;29=a²+c² => a²=29-c²

d2²=b²+c²; (√34)²=b²+c² ;34=b²+c² =>b²=34-c²

d²=c²+d4² ,где d4 - диагональ основания.

d4²=a²+b²

d²=c²+a²+b² ; (√38)²=c²+29-c²+34-c² ;

38= -c²+63

c²=63-38=25

c=√25=5 см

a²=29-c²=29-25=4

a=√4=2 см

b²=34-c²=34-25=9

b=√9=3 см

ответ: 2 см; 3 см

Answer 2

Finding the Sides of the Base of the Parallelepiped

To find the sides of the base of the parallelepiped, we can use the given information about the diagonals. Let's denote the sides of the base as a and b.

According to the problem, the diagonal of the parallelepiped is √38 cm, and the diagonals of the lateral faces are √29 cm and √34 cm.

We can use the Pythagorean theorem to relate the sides of the base and the diagonal of the parallelepiped:

a^2 + b^2 = 38 Similarly, we can use the Pythagorean theorem to relate the sides of the base and the diagonals of the lateral faces:

a^2 + b^2 = 29 a^2 + b^2 = 34

Solving the Equations

To find the sides of the base, we need to solve the system of equations formed by the above three equations.

Subtracting the second equation from the first equation, we get:

(a^2 + b^2) - (a^2 + b^2) = 38 - 29

Simplifying, we have:

0 = 9

This implies that the system of equations is inconsistent, which means there is no solution that satisfies all three equations simultaneously.

Therefore, based on the given information, we cannot determine the sides of the base of the parallelepiped.

Please let me know if there's anything else I can help you with!