Answer:
 BD = √97 cm ≈ 9.849 cm
Step-by-step explanation:
Diagonal BD of rectangle ABCD is the hypotenuse of right triangle ABD. Opposite sides of the rectangle are the same length, so we have ...
 AB = 4 cm
 AD = 9 cm
The sides are related to the diagonals by the Pythagorean theorem.
Pythagorean theorem
The Pythagorean theorem tells you the relation between sides and hypotenuse of a right triangle:
 AB² +AD² = BD²
 4² +9² = BD² = 16 +81 . . . . . evaluating the squares
 BD = √97 . . . . . take the square root
The length of BD is √97 cm, about 9.849 cm.
