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The length of a rectangular room is 8 feet greater than its width. The
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23 Feb 2023, 06:15
23 Feb 2023, 06:15
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Question Stats:
83% (01:21) correct
16% (03:44) wrong based on 18 sessions
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The length of a rectangular room is 8 feet greater than its width. The total area of the room is 240 square feet.
A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
Quantity A |
Quantity B |
The width of the room in feet |
12 |
A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
Re: The length of a rectangular room is 8 feet greater than its width. The
[#permalink]
19 Mar 2023, 01:25
19 Mar 2023, 01:25
Expert Reply
OE
Let L and W stand for the length and width of the room in feet. Then, from the first relation, you can write this equation:
(1) L = W + 8 Moreover, the area of a rectangle is given by length times width, such that:
(2) LW = 240
Taken together, you have two equations with two unknowns, and because the question involves the width rather than the length, you can eliminate the length by substituting from equation (1) into equation (2):
(W + 8)W = 240
Now expand the product and move everything to the left-hand side, so that you can solve the quadratic equation by factoring it. This gives:
\(W^2+8W=240\)
Solve
\((W+20)(W-12)=0\)
The two solutions are W = −20 and W = 12. A negative width does not make sense, so W must equal 12 feet. It is also possible to arrive at the answer by testing the value in Quantity B as the width of the room. Plug in 12 for W in equation (1): L = 12 + 8 = 20 feet If W = 12 and L = 20, then the area is (20)(12), which equals 240 square feet.
Because this agrees with the given fact, you may conclude that 12 feet is indeed the width of the room. Either method arrives at the conclusion. Therefore, the two quantities are equal.
Let L and W stand for the length and width of the room in feet. Then, from the first relation, you can write this equation:
(1) L = W + 8 Moreover, the area of a rectangle is given by length times width, such that:
(2) LW = 240
Taken together, you have two equations with two unknowns, and because the question involves the width rather than the length, you can eliminate the length by substituting from equation (1) into equation (2):
(W + 8)W = 240
Now expand the product and move everything to the left-hand side, so that you can solve the quadratic equation by factoring it. This gives:
\(W^2+8W=240\)
Solve
\((W+20)(W-12)=0\)
The two solutions are W = −20 and W = 12. A negative width does not make sense, so W must equal 12 feet. It is also possible to arrive at the answer by testing the value in Quantity B as the width of the room. Plug in 12 for W in equation (1): L = 12 + 8 = 20 feet If W = 12 and L = 20, then the area is (20)(12), which equals 240 square feet.
Because this agrees with the given fact, you may conclude that 12 feet is indeed the width of the room. Either method arrives at the conclusion. Therefore, the two quantities are equal.
gmatclubot
Re: The length of a rectangular room is 8 feet greater than its width. The [#permalink]
19 Mar 2023, 01:25
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