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Subject Test Math 1

Question 7 of 32

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SAT Subject Test

The figure presents square M N O P with horizontal base M P, such that P is to the right of M. Vertex N lies directly above M and vertex O lies directly above P. A vertical segment R T is drawn with R on N O and T on M P, such that R is closer to N than it is to O. A horizontal segment U S is drawn with U on M N and S on O P, such that U is closer to M than it is to N. The area of rectangle U N R Q is labeled “5 x.” The area of M U Q T is labeled “x squared.” The area of T Q S P is labeled “5 x.”

The figure above shows a square region divided into four rectangular regions, three of which have areas 5 x, 5 x, and x to the power of 2 end exponent, respectively. If the area of M N O P is 64, what is the area of
square Q R O S?

Select an Answer

9

Correct Answer: 
No

25

Correct Answer: 
Yes

30

Correct Answer: 
No

34

Correct Answer: 
No

39

Correct Answer: 
No

Since M N O P and Q R O S are squares, M N equals N O equals 8 and Q R equals R O. Thus, M U equals N R and the rectangle with area x to the power of 2 end exponent must be a square with sides of length x. The rectangles with area 5 x must have sides of length x and 5. Thus, the area of Q R O S is equal to 5 to the power of 2 end exponent equals 25.

Another approach is the following. Since Q R O S is a square, Q R equals R O. Thus, M U equals N R and M U Q T is a square with sides of length x. The rectangles with area 5 x must have sides of length x and 5. Since the area of M N O P is 64

table attributes columnalign right center left columnspacing 2px end attributes row cell open parentheses x plus 5 close parentheses squared end cell equals 64 row cell x squared plus 5 x plus 5 x plus 25 end cell equals 64 end table

Thus, the area of Q R O S is 25.

Question Difficulty: 
medium