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.

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)
==============
Cheers,
Stan H.
Answer by praseenakos@yahoo.com(507)   (Show Source): You can put this solution on YOUR website!
Question:

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,

Then you will get the same answers....

Hope you found the explanation useful...

Warm Regards.

Praseena.
Answer by Flake(45)   (Show Source): 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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