A quadrilateral in which the diagonals intersect at right angles have an area of 250 cm2.

A quadrilateral in which the diagonals intersect at right angles have an area of 250 cm2. Find its diagonals if it is known that one is 5 times larger than the other.

Let the length of the diagonal ВD = X cm, then, by condition, the length of the diagonal AC = 5 * X cm.
The area of a quadrilateral is half the product of its diagonals by the sine of the angle between the diagonals.
Savsd = ВD * AC * Sin900 * (1/2) = X * 5 * X * 1 = 250.
5 * X2 = 250 * 2 = 500.
X2 = 500/5 = 100.
X = ВD = 10 cm
AC = 5 * 10 = 50 cm.
Answer: The lengths of the diagonals are 10 cm and 50 cm.