Hi,

     .

A = lw

Question States***

(7m + x)(5m + x) = 3(7m)(5m)

35 + 12x + x^2 = 105

x^2 + 12x - 70 = 0 (tossing out negative solution for unit measure)

 x = 4.3 rounded

11.3m  by 9.3m are the dimensions of the new rectangle to the nearest tenth of a meter

 


 
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=424 is greater than zero. That means that there are two solutions: .

  

    

    

    

    Quadratic expression  can be factored:

  

  Again, the answer is: 4.295630140987, -16.295630140987.
Here's your graph:



 

 

Answer by Stitch(470)   (Show Source): You can put this solution on YOUR website!
 The area of a rectangle is equal to length x width.



 Area of original rectangle

 Area of original rectangle

The Area of the new rectangle is 3 times larger than the original.



The area of the new rectangle is 105 square meters.

Now lets write the are equation of the new rectangle.



Sub in the given values for L & W



Now we can use foil to simplify the equation

ERROR Algebra::Solver::Engine::invoke_solver_noengine: solver not defined for name 'foil'.


 
Error occurred executing solver 'foil' .




Now rewrite the equation



Set the equation to zero by subtracting 105 from both sides



Now we can use the quadratic equation



 
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=424 is greater than zero. That means that there are two solutions: .

  

    

    

    

    Quadratic expression  can be factored:

  

  Again, the answer is: 4.295630140987, -16.295630140987.
Here's your graph:





-------------------------------------

Since we can only have a positive distance, 4.3m is X.

Add 4.3m to both dimensions to find the new dimensions.







 

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