The figure above shows a rectangular parcel of undeveloped land partitioned into four regions, $$P, Q, R,$$ and $$S.$$

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The figure above shows a rectangular parcel of undeveloped land partitioned into four regions, $$P, Q, R,$$ and $$S.$$

by VJesus12 » Tue Sep 22, 2020 7:12 am

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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. $$20$$

Source: GMAT Paper Tests

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Re: The figure above shows a rectangular parcel of undeveloped land partitioned into four regions, $$P, Q, R,$$ and $$S. by Scott@TargetTestPrep » Fri Sep 25, 2020 1:49 pm VJesus12 wrote: Tue Sep 22, 2020 7:12 am AreaGeometry.PNG 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. $$20$$

Source: GMAT Paper Tests
Solution:

Since the area of region Q is x^2, the width of regions R and P is x. Since the area of region R is 5x, the length of R is 5x/x = 5, which is also one of the two dimensions of region S. Since the area of region P is 4x, the length of P is 4x/x = 4, which is also the other dimension of region S. Therefore, the area of region S is 5 * 4 = 20 sq. meters.

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