Find the diagonals of the parallelogram if the second diagonal is 8 cm and the sides are 4 cm, 6 cm.

Since we are given the values of the two sides and the value of the large diagonal, we can find the small diagonal by applying one of the parallelogram properties. Property: the sum of the squares of the diagonals is equal to the sum of the squares of the sides of the parallelogram. Let us denote the small diagonal by d, then the large diagonal by D and, accordingly, the sides by a and b. Based on the foregoing, we write down the formula: d ^ 2 + D ^ 2 = 2a ^ 2 + 2b ^ 2, therefore d = √ (2a ^ 2 + 2b ^ 2-D ^ 2), substitute the values: d = √ (2 * 4 ^ 2 + 2 * 6 ^ 2-8 ^ 2) = √ (32 + 64-64) = √32 = 4√2 (ue).
Answer: d = 4√2 (cu)