Praxis 5003 Practice Question
P = 2(L + W) The preceding formula gives the perimeter P of a rectangle with length L and width W. An outdoor patio is in the shape of a rectangle and has a perimeter of 48 feet. The width of the patio is 4 feet less than the length of the patio. What is the width, in feet, of the patio?
Correct Answer: A
Rationale: To solve for the width of the patio, define the length as \( L \) and the width as \( W = L - 4 \). Using the perimeter formula \( P = 2(L + W) \) and substituting the given perimeter of 48 feet, we have:
\[
48 = 2(L + (L - 4))
\]
This simplifies to \( 48 = 2(2L - 4) \), leading to \( 24 = 2L - 4 \). Solving for \( L \) gives \( L = 14 \). Consequently, \( W = 14 - 4 = 10 \).
Option A (10) is correct as it satisfies all conditions.
Option B (12) is incorrect because it does not fit the relationship \( W = L - 4 \).
Option C (20) and Option D (24) are both too large, failing to meet the perimeter requirement when substituted back into the perimeter formula.
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