Question 954995: A bedroom door has a perimeter of 28 feet and an area of 40 square feet. What are the dimensions of the door?
Answer by carmela(3)   (Show Source):
You can put this solution on YOUR website! Let:
L = length of the door
W = width of the door
P = perimeter
A = Area
Given:
P = 28 ft
A = 40 ft^2
Solution:
P = 2L + 2W since P = 28
28 = 2L +2W (equation 1)
A = LW since A = 40
40 = LW (equation 2)
Find L in equation 2, we have
L = 40 / W
Substitute L in equation 1
28 = 2 (40 / W) + 2W
Multiply both sides by W
28W = 2 (40) + 2W2
2W^2 - 28W +80 = 0
Divide both sides by 2
W^2 - 14W + 40 = 0
Factoring
(W – 4) ( W – 10) = 0
W = 4 and W = 10
Now we find L using the values of W.
If W = 4, then using equation 1
28 = 2L +2W
28 = 2L +2(4)
28 = 2L + 8
20 = 2L
L = 10
If W = 10, then using equation 1
28 = 2L +2W
28 = 2L +2(10)
28 = 2L + 20
8 = 2L
L = 4
We have 2 sets of solutions:
Solution Set 1 : L = 10 ft. and W = 4
Solution Set 1 : L = 4 ft. and W = 10 ft.
Although the 2 sets of solution are true if we substitute it both to the given perimeter and area, we need to pick one only.
In reality, the length of the bedroom door is always greater than the it’s width, so we are going to choose Solution Set 1.
Therefore the bedroom door has a length of 10 ft. and a width of 4ft.
I hope this helps :)
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