The diagonal of a rectangular closet floor is 7½ ft and its shorter side is 4½ ft. What is the area of the closet (in sq ft)?

Problem restatement
Use the Pythagorean relation to find the other side, then compute area.

Given data

• Diagonal d = 7.5 ft.
• Shorter side s = 4.5 ft.

Concept/Approach
For rectangle sides a and b: d² = a² + b². Let the unknown side be x.

Step-by-Step calculation
x = √(d² − s²) = √(7.5² − 4.5²) = √(56.25 − 20.25) = √36 = 6 ft Area = s × x = 4.5 × 6 = 27 sq ft

Verification/Alternative
Check: 4.5² + 6² = 20.25 + 36 = 56.25 = 7.5² (consistent).

Final Answer
27 sq ft