Question

The width of a rectangle is 3 feet shorter than its length. The perimeter is 530 feet. Let x equal the length of the rectangle. The formula is P = 2l + 2w. What are the length and the width of the rectangle? a. Write a list of the known information and the unknown information. Write an algebraic equation to show the relationship between the knowns and the unknowns. Solve the equation. Answer the question.

Answer 1

Known: perimeter = 530 feet.

Known: width = length - 3 feet

Known: it's a rectangle so

perimeter = 2×width + 2×length

Unknown: length and width

Equation:

530 feet = 2×width + 2×length

Substitute for width:

530 feet = 2×(length - 3 feet) + 2×length

If you insist on one character variable names and no units,

530 = 2(L-3) + 2L = -6 + 4L

536 = 4L

L = 134

530 feet = 2×length - 6 feet + 2×length

530 feet = 4×length - 6 feet.

(530 + 6) feet = 4×length

536 feet = 4×length

length = (536/4) feet = 134 feet

width = length - 3= 131 feet

The length of the rectangle is 134 feet.

The width of the rectangle is 131 feet.

Check: 2×134 + 2×131 = 268+262 = 530 feet