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The figure above shows a rectangular parcel of undeveloped land partitioned into four regions, P, Q, R, and S. In square meters, the area of square region Q is x^2, the area of rectangular region R is 5x, and the area of rectangular region P is 4x. What is the area, in square meters, of rectangular region S?
A. \((x^2) - x\)
B. \((x^2) + 9x\)
C. \(20x - (x^2)\)
D. \(9\)
E. \(20\)
Attachment:
AreaGeometry.PNG [ 3.47 KiB | Viewed 5400 times ]
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02 Nov 2018, 07:41
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Area of Q = \(x^2\) ; Side = x
Area of R = 5x = x * length ; length of R = 5
Area of P = 4x = x * width ; width of P = 4
Area of the entire plot =\((x+4) * (x+5) = x^2 + 9x + 20\)
Area of S = \(x^2 + 9x + 20 - x^2 - 5x - 4x = 20\)
Area of R = 5x = x * length ; length of R = 5
Area of P = 4x = x * width ; width of P = 4
Area of the entire plot =\((x+4) * (x+5) = x^2 + 9x + 20\)
Area of S = \(x^2 + 9x + 20 - x^2 - 5x - 4x = 20\)
02 Nov 2018, 13:54
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Just adding on an alternate method to what pandeyashwin did...if the algebra intimidates you, keep in mind that one helpful technique on any geometry problem its o just draw the shape and label it. If you do that:
1) Notice that the upper left panel (Q) is a square with area x^2, so each side of it is x.
2) Then since R has an area of 5x and you know that its vertical height is the same as the height of Q, so its height is x, then its other dimension is 5.
3) Same logic for P. You know its horizontal width is the same as Q so also x, so its horizontal width must be 4 in order for its area to be 4x.
That leaves you with this diagram in the end:
SubdividedRectangle.png [ 13.53 KiB | Viewed 4877 times ]
Note then that you know the dimensions of S: it has a height of 4 and a width of 5, so its area is 4 * 5 = 20.
1) Notice that the upper left panel (Q) is a square with area x^2, so each side of it is x.
2) Then since R has an area of 5x and you know that its vertical height is the same as the height of Q, so its height is x, then its other dimension is 5.
3) Same logic for P. You know its horizontal width is the same as Q so also x, so its horizontal width must be 4 in order for its area to be 4x.
That leaves you with this diagram in the end:
Attachment:
SubdividedRectangle.png [ 13.53 KiB | Viewed 4877 times ]
Note then that you know the dimensions of S: it has a height of 4 and a width of 5, so its area is 4 * 5 = 20.
