SOLUTION: Two rectangles A and B each have an area of 11 cm^2 The length of rectangle A is x cm The length of rectangle B is (x+3) cm Given that the width of rectangle A is 2 cm greater t

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Question 1145118: Two rectangles A and B each have an area of 11 cm^2
The length of rectangle A is x cm
The length of rectangle B is (x+3) cm
Given that the width of rectangle A is 2 cm greater than the width of rectangle B form an equation in x and show that it simplifies to
2x^2 + 6x - 33 = 0
Found 3 solutions by josmiceli, ikleyn, MathTherapy:
Answer by josmiceli(19441)   (Show Source): You can put this solution on YOUR website!
Let the width of B =
The width of A =
-----------------------------------
(1)
(2)
------------------------------------
(1)
and
{2}
(2)
------------------------------------
Set (1) = (2)

Multiply both sides by




--------------------------------
The sign of the constant term is different. Check my math.
Answer by ikleyn(52777)   (Show Source): You can put this solution on YOUR website!
.

            The solution by @josmiceli is INCORRECT. 

              His equation (2) is incorrect, leading to wrong answer.

            I came to bring the correct solution.


Solution 

From the condition, the width of rectangle  A  is   cm.

                    the width of rectangle  B  is  cm.


Also, from the condition


     -  = 2  cm.      (1)


It is your basic equation, and at this point, the setup is just completed.


Now my (and your) major task is to transform this equation to the standard form of a quadratic equation.


For it, multiply both side of the equation (1) by  x*(x+3).  You will get


    11*(x+3) - 11x = 2x*(x+3)

    11x + 33 - 11x = 2x^2 + 6x

    2x^2 + 6x - 33 = 0.


Your question is answered:  The equation in your post IS CORRECT.      ANSWER


Answer by MathTherapy(10551)   (Show Source): You can put this solution on YOUR website!

Two rectangles A and B each have an area of 11 cm^2
The length of rectangle A is x cm
The length of rectangle B is (x+3) cm
Given that the width of rectangle A is 2 cm greater than the width of rectangle B form an equation in x and show that it simplifies to
2x^2 + 6x - 33 = 0
With the length and area of rectangle A being x and 11, respectively, the width of rectangle A becomes: 

With the length and area of rectangle B being x + 3 and 11, respectively, the width of rectangle B becomes: 

As width of rectangle A is 2 cm GREATER than width of rectangle B, we get: 

11(x + 3) = 11x + 2x(x + 3) ------- Multiplying by LCD, x(x + 3)

 

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