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

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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. \(20\)

Answer: E

Source: GMAT Paper Tests

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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. \(20\)

Answer: E

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.

Answer: E

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