The area of a triangular park with sides 78 m, 160 m and 178 m is equal to the area of a rectangular garden whose sides are in the ratio of 13 : 12. The smaller side (in m) of the garden is:

A

$$26\sqrt{5}$$

B

$$24\sqrt{10}$$

C

$$12\sqrt{10}$$

D

$$13\sqrt{5}$$