Suppose u = and v = are two vectors that form the sides of a parallelogram. Then the lengths of the two diagonals of the parallelogram are?

| u | = √ (2² + (-1²)) = √5

| v | = √ (1² + (-8) ² = √65

cos (u, v) = (u * v) / (| u | * | v |) =

(2 * 1 + (-1) * ( - 8)) / √5 √ 65 = (2 + 8) / √5 √65 = 10 / (√5 √ 65)

The length of a larger diagonal:

d 1² = | u |² + 2 |u| |v| + | v |² = 5 + (2 √5 √65 * 10 / √5 √65) + 65

d 1² = 70 + 20 = 90

d 1 = √ 90 = 3√10

d 2² = 70 - 20 = 50

d 2 = √50 = 5√2

Answer:

The lengths of the diagonals are: 3√10 and 5√2.