Question 242827: The rectangle ABCD has sides that are parallel to the coordinate axes. It is three times as wide as it is tall, and its perimeter is 56 units.
Find the length and width of ABCD. Given the information D=(9,2), find the coordinates for points A, B and C.
Answer by oberobic(2304)   (Show Source):
You can put this solution on YOUR website! The question asks you to find the length and width of a rectangle that is 3 times as wide as it is tall.
Since it is a rectangle and parallel to the coordinate axis, we are confident in defining:
w = width
h = height = 3w
We will not use 'h' in the solution proper, but instead we will use w and 3w to keep to one unknown.
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We are told that the perimeter = 56.
We know the perimeter = 2w + 2h for all rectangles.
Substituting 3w for h, we have
56 = 2w + 2(3w)
56 = 2w + 6w
56 = 8w
7 = w
w = 7
Substituting for w, we have
h = 3w = 3(7) = 21
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Now we know that point D is at (9,2), which is one corner.
Assuming it is the lower right corner, the coordinates can be calculated.
A = (9-w, 2) = (2,2)
B = (9-w, 2+h)= (2,23)
C = (9, 2+h) = (9, 23)
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