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28 Mar 2023, 01:30
Kudos
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C
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Difficulty:
35%
(medium)
Question Stats:
75% (02:37) correct
25%
(02:42)
wrong
based on 36
sessions
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A piece of wire used to fence a rectangular land can be used to fence a square land that has twice the width of the rectangular land.What is the area of the square land if the area of the rectangular land is 100 sq units less than the area of the square land?
A. 100 sq units
B. 300 sq units
C. 400 sq units
D. 900 sq units
E. 1000 sq units
A. 100 sq units
B. 300 sq units
C. 400 sq units
D. 900 sq units
E. 1000 sq units
28 Mar 2023, 02:09
Kudos
Bookmarks
Bunuel
Length of the rectangular plot = L
Width of the rectangular plot = W
Dimension of the square plot = 4W
A piece of wire used to fence a rectangular land can be used to fence a square land that has twice the width of the rectangular land
The statement tells us that the perimeter of the rectangular plot and the square plot is the same
\(2(L + W) = 4*2W\)
\(L = 3W\)
\(W = \frac{L}{3}\)
the area of the square land if the area of the rectangular land is 100 sq units less than the area of the square land
\((2W)^2 - (LW) = 100\)
\(W(4W - L) = 100\)
\(\frac{L}{3}(4*\frac{L}{3} - L) = 100\)
L = 30
\(W = \frac{L}{3} = 10\)
Dimension of square = 2W = 20
Area of square = 20 * 20 = 400 sq units
