In a rectangular parallelepiped, the side edge is 12 cm, the area of the diagonal section is 312 cm²
August 24, 2021 | education
| In a rectangular parallelepiped, the side edge is 12 cm, the area of the diagonal section is 312 cm², and the area of the base of this parallelepiped is 240 cm². Calculate the sides of the base.
Since the area of the diagonal section is 312 cm ^ 2, the diagonal of the base is:
312: 12 = 26 cm.
We take the sides y of the base for x, then we get the system of equations:
x * y = 240;
x ^ 2 + y ^ 2 = 26 ^ 2.
Express x from the first and substitute it into the second:
x = 240 / y;
240 ^ 2 / y ^ 2 + y ^ 2 = 26 ^ 2;
y ^ 4 – 26 ^ 2 * y ^ 2 – 240 ^ 2 = 0;
y ^ 2 = 36;
y = 6.
Then:
x = 240: 6 = 40.
Answer: the sides of the base are 6 and 40 cm.
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