The perimeter of an isosceles triangle is 91 cm, and its base is $$1\frac{1}{4}$$ times each of its equal sides. What is the length (in cm) of its base?

Let each of the equal sides of the isosceles triangle be (x) cm.
The base is given as $$1\frac{1}{4}$$ times each equal side.

Converting the mixed fraction into an improper fraction:

$$\frac{1}{4}=\frac{5}{4}$$

So, the base of the triangle is:

$$\frac{5}{4}x$$

The perimeter of the triangle is 91 cm, therefore:

$$x+x+\frac{5}{4}x=91$$

$$2x+\frac{5}{4}x=91$$

$$\frac{8x+5x}{4}=91$$

$$\frac{13x}{4}=91$$

$$13x=364$$

$$x=28$$

Thus, each equal side is 28 cm.

Now, the base is:

$$\frac{5}{4}\times 28=35$$

Hence, the base length is 35 cm.