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04 Jan 2021, 09:00
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Length
(m): 5 Width
(m): 4
(m): 5 Width
(m): 4
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
15%
(low)
Question Stats:
86% (02:18) correct
14%
(03:13)
wrong
based on 1042
sessions
History
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Result
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Andy is considering enlarging his existing garden, which is rectangular. He has two options. If he increases the length of the existing garden by 5 m and does not change the width, then the area of the enlarged rectangular garden will be twice the area of the existing garden. On the other hand, if he increases the width of the existing garden by 2 m and does not change the length, then the area of the enlarged rectangular garden will be 1.5 times the area of the existing garden.
From the Dimensions column in the following table, identify a length and a width, in meters, for Andy's existing garden that are consistent with Andy's two options. Make only two selections, one in for each column.
From the Dimensions column in the following table, identify a length and a width, in meters, for Andy's existing garden that are consistent with Andy's two options. Make only two selections, one in for each column.
|
Length (m) |
Width (m) |
Dimensions |
| 3 | ||
| 4 | ||
| 5 | ||
| 6 | ||
| 7 | ||
| 8 |
ShowHide Answer
Official Answer
Length
(m): 5 Width
(m): 4
(m): 5 Width
(m): 4
11 Jan 2021, 23:00
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Official Explanation
RO1
For any rectangle, the area is equal to the length (L) times the width (W). In Andy's garden, a length 5 m longer would yield an area twice as large. In other words, (L + 5)W = 2LW. Distributing the W gives LW + 5W = 2LW, and subtracting LW from both sides gives 5W = LW.
We are also told that a width 2 m longer would yield an area 1.5 times as large. In other words, L(W + 2) = 1.5LW. Distributing the L gives LW + 2L = 1.5LW, and subtracting 1.5LW from both sides gives 2L = 0.5LW. Multiplying both sides of the equation by 2 gives 4L = LW.
Thus, 5W = LW and 4L = LW, so 5W = 4L. Dividing both sides of the equation by 5 gives \(W=\frac{4}{5}L.\) The following table shows what the width of Andy’s garden would be for each of several possible lengths:
The only value for the width that is one of the possible options is 4. The corresponding length is 5.
The correct answer is 5.
RO2
The table provided in the analysis of RO1 shows that if the length is 5, the corresponding width is 4.
The correct answer is 4
RO1
For any rectangle, the area is equal to the length (L) times the width (W). In Andy's garden, a length 5 m longer would yield an area twice as large. In other words, (L + 5)W = 2LW. Distributing the W gives LW + 5W = 2LW, and subtracting LW from both sides gives 5W = LW.
We are also told that a width 2 m longer would yield an area 1.5 times as large. In other words, L(W + 2) = 1.5LW. Distributing the L gives LW + 2L = 1.5LW, and subtracting 1.5LW from both sides gives 2L = 0.5LW. Multiplying both sides of the equation by 2 gives 4L = LW.
Thus, 5W = LW and 4L = LW, so 5W = 4L. Dividing both sides of the equation by 5 gives \(W=\frac{4}{5}L.\) The following table shows what the width of Andy’s garden would be for each of several possible lengths:
The only value for the width that is one of the possible options is 4. The corresponding length is 5.
The correct answer is 5.
RO2
The table provided in the analysis of RO1 shows that if the length is 5, the corresponding width is 4.
The correct answer is 4
Attachment:
2.jpg [ 11.45 KiB | Viewed 16010 times ]
General Discussion
04 Jan 2021, 10:12
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Let's consider that length of the garden be L meters and width be W meters.
From the given information :
Increase the length by 5 meter and keep width unchanged .
Area : (L+5)(W) = 2 x (L)(W) --- 1
Increase the width by 2 meter and keep length unchanged .
Area : (L)(W+2) = 1.5 x (L)(W). --- 2
From 1 and 2 together (putting 2 into 1)
3x(L+5)(W) = 4x (L)(W+2)
3LW + 15W = 4LW + 8L
L(W+8) = 15W
L = 15W/(W+8)
Let W= 3, L will be 45/11
W=4, L will be 60/12 = 5
W=5, L will be 75/13
W= 6, L will be 90/14
W= 7, L will be 105/15 = 7 (For two selections,one in for each column L and W can't be same)
W=8 L will be 120/16= 7.5 (width can't be greater than Length)
Hence,
Length = 5
Width = 4
From the given information :
Increase the length by 5 meter and keep width unchanged .
Area : (L+5)(W) = 2 x (L)(W) --- 1
Increase the width by 2 meter and keep length unchanged .
Area : (L)(W+2) = 1.5 x (L)(W). --- 2
From 1 and 2 together (putting 2 into 1)
3x(L+5)(W) = 4x (L)(W+2)
3LW + 15W = 4LW + 8L
L(W+8) = 15W
L = 15W/(W+8)
Let W= 3, L will be 45/11
W=4, L will be 60/12 = 5
W=5, L will be 75/13
W= 6, L will be 90/14
W= 7, L will be 105/15 = 7 (For two selections,one in for each column L and W can't be same)
Hence,
Length = 5
Width = 4
