SOLUTION: the length of a rectangle is 2 more than twice its width. if the area of the rectangle is 24 square meters, find its dimension

Question 950670: the length of a rectangle is 2 more than twice its width. if the area of the rectangle is 24 square meters, find its dimension
Found 2 solutions by macston, Gogonati:
Answer by macston(5194) (Show Source): You can put this solution on YOUR website!
W=width; L=length=2W+2; A=area=L*W=24 sq m
A=L*W Substitute for L
24 sq m=(2W+2)(W)
Subtract 24 sq m from each side

Solved by pluggable solver: SOLVE quadratic equation with variable

Quadratic equation (in our case ) has the following solutons:

For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=196 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 3, -4. Here's your graph:

W=3 ANSWER 1: The width is 3 meters.
L=2W+2=2(3m)+2=6m+2m=8m ANSWER 2: Length is 2 meters.
CHECK:
Area=L*W=24 sq m
8m*3m=24 sq m
24 sq m=24 sq m

Answer by Gogonati(855) (Show Source): You can put this solution on YOUR website!
Let the width be x m, than the length will be 2x+2 m. The area of the rectangle will be: x(2x+2)=24. Solving this quadratic equation we get:
x^2+ x-12=0
(x+4)(x-3)=0
{-4, 3}
Since the dimension is always positive, the width of the rectangle is 3 m, and the length is 8m.
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