Question

The length of 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. If a circular board is carved such that its area is 44.44% of the area of the closet, what is the area of the circular board (in square feet)?

• A.
• B.
• C. 27
• D. 15
• E. None of these

Answer 1

The correct option is E

None of these

Other side = $\sqrt{{{}^{\left(\frac{15}{2}\right)}}^2{{-}^{\left(\frac{9}{2}\right)}}^2}$ ft = $\sqrt{\frac{225}{4}-\frac{81}{4}}$ ft = $\sqrt{\frac{144}{4}}$ ft = 6 ft
Area of the closet = (6 $\times$ 4.5) sq.ft = 27 sq.ft
$\therefore$ Area of the circular board = $\frac{4}{9}\times 27$ sq.ft = $12$ sq.ft