GeminiHeat wrote:
Attachment:
11.jpg
To cover the floor of an entry hall, a 1′ * 12′ strip of carpet is cut into two pieces, shown as the shaded strips in the figure above, and each piece is connected to a third carpet piece as shown. If the 1′ strips run parallel to each other, what is the total area of the carpeted floor, in square feet?
(A) 46
(B) 48
(C) 52.5
(D) 56
(E) 60
Is it option E, 60?
Explanation:
Strip of Carpet has Length as 12 ft and width as 1 ft
Let us cut this strip into 2 pieces of A ft and (12 - A) ft
Area of Upper strip = A ft x 1 ft = A\(ft^2\)
Area of Lower strip = (12 - A) ft x 1 ft = (12 - A) \(ft^2\)
As we can see, height of the Middle part is 8 ft (10 - 1 - 1)
So, Area of Middle part = \(\frac{1}{2}\) x [A + (12 - A)] x 8 = \(\frac{1}{2}\) x 12 x 8 = 48 \(ft^2\)
Total Area = Area of Upper strip + Area of Middle part + Area of Lower strip
Total Area = A + (12 - A) + 48 = 12 + 48 = 60 \(ft^2\)
Hence, option E