The sum of all strictly parallelograms is 10, and their difference is 6. What is the sum of the squares
| September 2, 2021 | education
The sum of all strictly parallelograms is 10, and their difference is 6. What is the sum of the squares of the diagonals of the parallelogram?
By condition, the sum of adjacent sides is 10 cm.
AB + AD = 10 cm.
And their difference is 6.
AD – AB = 6 cm.
Let’s solve the system of two equations by the addition method.
AB + AD + AD – AB = 10 + 6.
2 * AD = 16.
AD = 8 cm.
AB = 10 – 8 = 2 cm.
Since the sum of the squares of the diagonals is equal to twice the sum of the squares of the adjacent sides, then
AC ^ 2 + BD ^ 2 = 2 * (AB ^ 2 + AD ^ 2).
AC ^ 2 + BD ^ 2 = 2 * 68.
AC ^ 2 + BD ^ 2 = 136.
Answer: The sum of the squares of the diagonals is 136 cm2.
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