Find the diagonal of a parallelogram with sides 6 and 8 cm if the length of the second diagonal is 12 cm.

As we know from the geometry course taught at the school, a figure of this type has the property that the sum of the squares of its sides will be the same as the sum of the squares of its diagonals.

Let us determine with the help of how many centimeters it will be possible to express the length of the diagonal of our geometric figure, when it is known from the condition that it has sides of 6 and 8 cm, respectively, and a diagonal of 12 cm:

d1 ^ 2 = 2 * (6 ^ 2 + 8 ^ 2) – 12 ^ 2;

d1 ^ 2 = 2 * (36 + 64) – 144;

d1 ^ 2 = 56;

d11 = 2√14;

d12 = -2√14 (not suitable).

Answer: 2√14 cm.