alleryStart learning →The perimeter of a rectangle is 40. The length is 4 more than the width. Find the length and width.
ALength 8 and width 12
BLength 10 and width 10
CLength 12 and width 8
DLength 14 and width 6
Answer & Solution
Correct answer: C. Length 12 and width 8
1. Let L be the length and W be the width, giving the system 2L + 2W = 40 and L = W + 4.
2. Substitute W + 4 for L in the perimeter equation: 2(W plus 4) plus 2W equals 40.
3. Distribute and simplify: 2W plus 8 plus 2W equals 40, so 4W equals 32, giving W equals 8.
4. Substitute W = 8 into L = W + 4 to get L equals 12, and checking confirms 2(12) plus 2(8) equals 40.
_Source: OpenStax Elementary Algebra (CC BY 4.0), Ch 5 "Systems of Linear Equations", section 5.4 Solve Applications with Systems of Equations_
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