Rectangle with diagonal and one side in mixed numbers\nThe diagonal of a rectangular closet floor is 7½ feet. The shorter side is 4½ feet. Find the area of the closet (in square feet).

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:

Verification / 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