fozzzy wrote:
Attachment:
image.jpg
The figure above represents a square plot measuring x feet on a side. The plot consists of a rectangular garden, 48 square feet in area, surrounded by a walkway that is 3 feet wide on two opposite sides and 2 feet wide on the other two sides. What is the value of X?
a) 8
b) 10
C) 12
d) 16
e) 18
Work from the answer choices. I'll pretend I started with E.
If x = 18, the length of the rectangle must be 18 - 2 - 2 (for each part of the walkway) = 14
OR 18 - 3 - 3 = 12 is the length of the rectangle.
Work with 12; it's a factor of 48, the area of the rectangle.
If rectangle length = 12, width is 48/12 = 4.
But that's the side that has 2-foot wide walkways.
Adding both 2-foot walkway parts to the width of the rectangle should yield 18.
4 + 2 + 2 = 8. Not possible. The outside shape is a square. Sides must be equal. 18 and 8 aren't equal.
No need to test rectangle length or width of 14. If 18 were the answer, because the outside is a square, it would yield 18 after taking walkway into account no matter which measure of rectangle side were used.
Try C, x = 12. If so, length of rectangle is 12 - 2 - 2 = 8. (Or 12 - 3 - 3 = 6.)
Work with L=8. If so, rectangle width must be 48/8 = 6.
When calculating rectangle length = 8, we accounted for the two 2-foot wide walkway parts.
So to rectangle width of 6, add the two 3-foot parts of the walkway: 3 + 3 = 6.
6 + 6 = 12, which is the number we need to make the sides be equal.
Answer C (which I chose to test first - got lucky)
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