Area of the second playground: $64 \times 48 = 3072$ square meters.

The first playground has width 24 m and the same area:

$24 \times \text{length} = 3072$

$\text{length} = \dfrac{3072}{24} = 128$ meters.

Perimeter $= 2(24 + 128) = 2 \times 152 = \mathbf{304}$ meters.