Rectangle with diagonal and one side in mixed numbers The diagonal of a rectangular closet floor is 7½ feet. The shorter side is 4½ feet. Find the area of the closet (in square feet).
Aptitude
Area
Difficulty: Easy
Choose an option
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A9
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B18
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C27
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D36
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ENone of these
Answer
Correct Answer: 27
Explanation
Introduction / Context:Using the Pythagorean theorem on a rectangle (right triangle formed by sides and diagonal), we can find the unknown side and then compute the area as product of the two sides.
Given Data / Assumptions:
- Diagonal d = 7.5 ft
- Shorter side s1 = 4.5 ft
- Other side s2 unknown
Concept / Approach:For rectangle sides s1 and s2, d^2 = s1^2 + s2^2 ⇒ s2 = sqrt(d^2 − s1^2). Area = s1 * s2.
Step-by-Step Solution:
s2 = sqrt(7.5^2 − 4.5^2) = sqrt(56.25 − 20.25) = sqrt(36) = 6 ft Area = 4.5 * 6 = 27 sq ftVerification / Alternative check:Pythagoras check: 4.5^2 + 6^2 = 20.25 + 36 = 56.25 = 7.5^2 (consistent).
Why Other Options Are Wrong:9, 18, and 36 sq ft do not match the exact side computed from the diagonal relation.
Common Pitfalls:Misreading mixed numbers (7 1/2 as 7.12) or arithmetic mistakes when squaring/ subtracting undermine accuracy.
Final Answer:27