SOLUTION: Solve algebraically using only one variable. The length of a rectangle is two more than twice its width. If the area of the rectangle is 84, find the length and width.
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Question 86695: Solve algebraically using only one variable. The length of a rectangle is two more than twice its width. If the area of the rectangle is 84, find the length and width. Found 3 solutions by stanbon, praseenakos@yahoo.com, Flake:Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website! Solve algebraically using only one variable. The length of a rectangle is two more than twice its width. If the area of the rectangle is 84, find the length and width.
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Let the width be x; then the length is 2x+2
EQUATION:
Area = width*length
84 = x(2x+2)
42 = x(x+1)
x^2+x-42=0
(x+7)(x-6)=0
Positive answer:
x=6 (width)
2x+2 = 14 (length)
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Cheers,
Stan H.
Solve algebraically using only one variable. The length of a rectangle is two more than twice its width. If the area of the rectangle is 84, find the length and width.
Answer:
Assume that width of the rectangle = x units.(since here length is given in terms of width...so first assume width = x units)
Then twice the width = 2*x = 2x
Two more than twice the width = 2x + 2
Then length of the rectangle = 2x + x units
Now area of the triangle is given as = 84
By the formula, area = length * width
==> length * width = 84
==> (2x + 2 ) * x = 84
Remove the parenthesis....
==> 2x * x + 2 * x = 84
==>
This is a quadratic equation....you can solve it by either factorisation method or using quadratic formula...
Factorisation method....
Here you have to find out two numbers whose sum is 1 and their product is -42
Such two numbers are 7 and -6
Now split the middle terms using this numbers.....
Now group the terms....
Now take out the common term from each group.....
Here (x+ 7 ) is common ib both the groups...so again take it outside...
==> (x + 7)( x- 7) = 0
==> either x + 7 = 0 or x - 6 = 0
==> x = -7 or x = 6
So the solution of the given expression is x = -7 or x = 6
You can check the answers using quadratic formula,
You can put this solution on YOUR website! --Given#1: "length (L) is two more than twice its width (W)"
What this means is---> L = 2+2W
--Given#2: Area of the rectangle is 84
What this means is --> Area of rectangle = LW = 84
--Solution:
--Step#1: Start with Area: LW=84
--Step#2: Replace L with Given#1 ----> (2+2W)W = 84
--Step#3: Expand (2+2W)W = 84
2W+2W^2 = 84
2(W+W^2) = 84
W+W^2 = 42
W^2 + W -42 = 0
(W+7)(W-6) = 0
W= "-7" or 6
Since length of rectangle can't be "negative", then W must be 6
--Step#4: Substitude W=6 to Given#2
LW=84
L(6)=84
L=84/6
L=14
--Check#1: L = 2+2W
14 = 2+2(6)---Yes
--Check#2: LW=84
14(6)=84---Yes
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