The diagonal of the floor of a rectangular closet is $$7\frac{1}{2}$$ feet. The shorter side of the closet is $$4\frac{1}{2}$$ feet. What is the area of the closet in square feet?
The diagonal of the floor of a rectangular closet is $$7\frac{1}{2}$$ feet. The shorter side of the closet is $$4\frac{1}{2}$$ feet. What is the area of the closet in square feet? Correct Answer 27 sq. ft.
$$\eqalign{ & {\text{Outer}}\,{\text{Side}} \cr & = \sqrt {{{\left( {\frac{{15}}{2}} \right)}^2} - {{\left( {\frac{9}{2}} \right)}^2}ft} \cr & = \sqrt {\frac{{225}}{4} - \frac{{81}}{4}ft} \cr & = \sqrt {\frac{{144}}{4}ft} \cr & = 6ft \cr & \therefore {\text{Area}}\,{\text{of}}\,{\text{closet}} = \left( {6 \times 4.5} \right)sq.\,ft = 27\,sq.\,ft. \cr} $$
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Feb 20, 2025