The perimeter of a rectangle is 84 feet. the length is two feet greater than 3 times the width. find the length and width. draw and label a diagram.

The formula for a rectangle's perimeter is

P = 2l + 2w

We know the length is 2 ft greater than thrice the width, so 2l becomes:

3w + 2ft + 3w + 2ft

Substitute.

P = 3w + 2ft + 3w + 2ft + 2w

Add like terms.

P = 8w + 4ft

Substitute P.

84 ft = 8w + 4ft

Subtract 4 ft from both sides to eliminate. (Property of equality)

84 ft - 4ft = 8w + 4ft - 4ft
80 ft = 8w

Divide 8 on both sides to isolate w.

80 ft / 8 = 8w / 8

10 ft = w

We have the value of w, now look for the l which we know is 2 feet more than thrice the value of w.

l = 10 ft × 3 + 2 ft
l = 30 ft + 2 ft
l = 32 ft

Therefore, the length and the width of the rectangle is 10 ft (w) and 32 ft (l).

Check:
84 ft = (2) (10 ft) + (2) (32 ft)
84 ft = 20 ft + 64 ft
84 ft = 84 ft ✔

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