A rectangular playground is 20 m longer than it is wide. A walking track of uniform width 2 m is laid all around the playground. The area of the walking track is 176 m². What is the perimeter of the playground (excluding the track)?
80 m
Let width = W, length = W + 20.
Outer dimensions (including the 2 m track all around) = (W + 24) × (W + 4). Wait, adding 2 m on each side adds 4 m to each dimension: outer length = (L + 4), outer width = (W + 4).
Area of track = (L + 4)(W + 4) - LW = 176. Expanding: 4L + 4W + 16 = 176, so L + W = 40.
Since L = W + 20, we get W + 20 + W = 40, so W = 10 and L = 30.
Perimeter of the playground = 2(L + W) = 2 × 40 = 80 m.
Hence, the perimeter of the playground is 80 m.
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