The length of a rectangular building is 6 feet less than 3 times the width. The perimeter is 120 fee

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The length of a rectangular building is 6 feet less than 3 times the width. The perimeter is 120 feet. Find the width and length of the building.

P = 2l + 2w
Since P = 120, we have:
(1) 2l + 2w = 120

We are also given:
(2) l = 3w - 6

Substitute equation (2) into equation (1)
2(3w - 6) + 2w = 120

Multiply through:
6w - 12 + 2w = 120

Combine like terms:
8w - 12 = 120

Add 12 to each side:
8w = 132

Divide each side by 8 to isolate w:
w =16.5

Now substitute w into equation (2)
l = 3(16.5) - 6
l = 49.5 - 6
l = 43.5

So (l, w) = (43.5, 16.5)