Farmer Brown wants to double the size of his rectangular backyard vegetable patch by adding a strip (of the same width) all the way around it. If its current patch is 12 feet by 18 feet, how wide does the strip need to be?
3ft
To double the size of the rectangular backyard vegetable patch, we need to add a strip of the same width all the way around it. Let's say the width of the strip is 'x' feet.
The current patch is 12 feet by 18 feet. After adding the strip around it, the new dimensions will be increased by twice the width of the strip.
So, the new dimensions of the patch will be (12 + 2x) feet by (18 + 2x) feet.
We want the new patch to be double the size of the current patch, so the new dimensions should be twice the dimensions of the current patch:
(12 + 2x) feet = 2 * 12 feet = 24 feet
(18 + 2x) feet = 2 * 18 feet = 36 feet
Simplifying the equations, we have:
12 + 2x = 24
18 + 2x = 36
Subtracting 12 from both sides of the first equation and 18 from both sides of the second equation, we get:
2x = 12
2x = 18
Dividing both sides of each equation by 2, we get:
x = 6
x = 9
So, the width of the strip needs to be either 6 feet or 9 feet.
To find out how wide the strip needs to be, we need to determine the increase in width and length of the vegetable patch.
Currently, the vegetable patch measures 12 feet by 18 feet. To double the size of the patch, we need to increase both the width and length by the same amount.
Let's assume the width of the strip is represented by 'x' feet.
To find the increased width, we add the width of the strip to both sides of the original width:
12 feet (original width) + 2x feet (strip width on both sides) = 12 + 2x feet
For the increased length, we add the strip width to both ends of the original length:
18 feet (original length) + 2x feet (strip width on both ends) = 18 + 2x feet
Since the increased width and length are the same, we can set them equal to each other:
12 + 2x = 18 + 2x
By subtracting 2x from both sides:
12 = 18
This equation is not possible since it results in an incorrect statement. Therefore, there is no solution to this problem.
Hence, it is not possible to double the size of Farmer Brown's rectangular backyard vegetable patch by adding a strip of the same width all the way around it.