Area=legnth times width
legnth is 1 less than 2 times width
l=legnth
w=width
l=-1+2w
l=2w-1
area=lw
area=45
subsitute
45=lw
45=(2w-1)w
distribute
45=2w^2-w
subtract 45 from both sides
0=2w^2-w-45
factor because if we have xy=0 and we factor we can assume that x and/or y=0 so
trial and error factor
0=(2w+9)(w-5)
set each to zero
0=2w+9
subtract 9
-9=2w
divide 2
-4.5=w
impossible since width cannot be negative so discard
w-5=0
add 5 to both sides
w=5
true
subsitute
l=2w-1
l=2(5)-1
l=10-1
l=9
w=5 cm
l=9 cm
Answer:
which class question is this
The first thing we must do for this case is to find the relationship between the variables.
We have then:
![AB = DC\\4y - 2 = 2y + 6](https://tex.z-dn.net/?f=%20AB%20%3D%20DC%5C%5C4y%20-%202%20%3D%202y%20%2B%206%20%20)
From here, we clear the value of "Y":
![4y - 2y = 6 + 2\\2y = 8](https://tex.z-dn.net/?f=%204y%20-%202y%20%3D%206%20%2B%202%5C%5C2y%20%3D%208%20%20)
![y = \frac{8}{2}\\y = 4](https://tex.z-dn.net/?f=%20y%20%3D%20%5Cfrac%7B8%7D%7B2%7D%5C%5Cy%20%3D%204%20%20%20)
On the other hand we have:
![AD = BC\\3x - 1 = 2x + 2](https://tex.z-dn.net/?f=%20AD%20%3D%20BC%5C%5C3x%20-%201%20%3D%202x%20%2B%202%20%20)
From here, we clear the value of "x":
![3x - 2x = 2 + 1\\x = 3](https://tex.z-dn.net/?f=%203x%20-%202x%20%3D%202%20%2B%201%5C%5Cx%20%3D%203%20%20)
Then, replacing values we have:
![AB = DC = 4y - 2 = 4 (4) - 2 = 16 - 2 = 14\\AB = DC = 14](https://tex.z-dn.net/?f=%20AB%20%3D%20DC%20%3D%204y%20-%202%20%3D%204%20%284%29%20-%202%20%3D%2016%20-%202%20%3D%2014%5C%5CAB%20%3D%20DC%20%3D%2014%20%20)
On the other hand:
![AD = BC = 2x + 2 = 2 (3) + 2 = 6 + 2 = 8\\AD = BC = 8](https://tex.z-dn.net/?f=%20AD%20%3D%20BC%20%3D%202x%20%2B%202%20%3D%202%20%283%29%20%2B%202%20%3D%206%20%2B%202%20%3D%208%5C%5CAD%20%3D%20BC%20%3D%208%20%20)
Finally, the perimeter is given by:
![P = AB + DC + AD + BC](https://tex.z-dn.net/?f=%20P%20%3D%20AB%20%2B%20DC%20%2B%20AD%20%2B%20BC%20%20)
Substituting values we have:
![P = 14 + 14 + 8 + 8\\P = 44](https://tex.z-dn.net/?f=%20P%20%3D%2014%20%2B%2014%20%2B%208%20%2B%208%5C%5CP%20%3D%2044%20%20)
Answer:
the perimeter of ABCD is:
44 units