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Difficulty:
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40% (03:27) correct
60%
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wrong
based on 462
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A rectangular yard is 20 yards wide and 40 yards long. It is surrounded by a thick hedge that grows on the border of the property, but completely within the boundaries of the yard. If the hedge covers an area of 171 square yards, what is the width of the hedge?
A. 160/120
B. 170/120
C. 180/120
D. 191/120
E. 800/120
A. 160/120
B. 170/120
C. 180/120
D. 191/120
E. 800/120
07 Apr 2012, 05:40
Kudos
Bookmarks
A rectangular yard is 20 yards wide and 40 yards long. It is surrounded by a thick hedge that grows on the border of the property, but completely within the boundaries of the yard. If the hedge covers an area of 171 square yards, what is the width?
A. 160/120
B. 171/120
C. 180/120
D. 191/120
E. 800/120
The area of the whole yard is 20*40=800 square yards;
The area of the uncovered yard is 800-171=629 square yards (the whole area minus the area of the portion of the yard which is covered by the hedge);
Now, the width of the uncovered yard is 20-2x and the length is 40-2x, so its area is (20-2x)(40-2x)=629 --> (20-2x)(40-2x)=17*37. At this point it's better to substitute the values from answer choices rather than to solve for x. Answer choice C, 3/2 fits.
Answer: C.
Garden.png [ 3.94 KiB | Viewed 24783 times ]
A. 160/120
B. 171/120
C. 180/120
D. 191/120
E. 800/120
The area of the whole yard is 20*40=800 square yards;
The area of the uncovered yard is 800-171=629 square yards (the whole area minus the area of the portion of the yard which is covered by the hedge);
Now, the width of the uncovered yard is 20-2x and the length is 40-2x, so its area is (20-2x)(40-2x)=629 --> (20-2x)(40-2x)=17*37. At this point it's better to substitute the values from answer choices rather than to solve for x. Answer choice C, 3/2 fits.
Answer: C.
Attachment:
Garden.png [ 3.94 KiB | Viewed 24783 times ]
General Discussion
30 Jul 2004, 01:39
Kudos
Bookmarks
Let n be the width of the hedge and assuming it grows uniformly
the 40(20) - (40-2n)(20-2n) = 171
4n^2 - 120n +171 = 0
Solving for n gives 1.5 or 28.5
From the choices, (C) is 1.5.
No choices gave n as 28.5, so (C) is the answer.
the 40(20) - (40-2n)(20-2n) = 171
4n^2 - 120n +171 = 0
Solving for n gives 1.5 or 28.5
From the choices, (C) is 1.5.
No choices gave n as 28.5, so (C) is the answer.
