Half the perimeter of a rectangular garden is 36 m. Its length is 4 m more…

Concept

For a rectangle with length L and width W, the perimeter is 2(L + W); therefore, the half-perimeter is L + W.

If the length is d units more than the width, the relation is L = W + d.

Application

1. Let W metres be the width. Then L = W + 4 metres.

2. The half-perimeter is 36 m, so L + W = 36.

3. Substitute L = W + 4: (W + 4) + W = 36, hence 2W + 4 = 36.

4. Subtract 4 from both sides: 2W = 32. Dividing by 2 gives W = 16 m.

5. Therefore, L = W + 4 = 16 + 4 = 20 m.

Cross-check

The dimensions 20 m and 16 m have half-perimeter 20 + 16 = 36 m and differ by 20 - 16 = 4 m, so both conditions hold.

Result

The length of the garden is 20 m.