The area of the rhombus is 27. One diagonal is 1.5 times smaller than the other. Find the big diagonal.

Let the smaller diagonal ВD of the rhombus AВСD be equal to X cm. VD = X cm.

Then, by condition, the large diagonal AC = 1.5 * X cm.

The area of a rhombus is equal to half the products of the lengths of its diagonals.

Sasvd = AC * СD / 2.

27 = 1.5 * X * X / 2 = 1.5 * X^2 / 2.

X2 = 2 * 27 / 1.5 = 36.

X = √36 = 6 cm.

Then AC = 1.5 * 6 = 9 cm.

Answer: The length of the larger diagonal is 9 cm.