Alice drew a rectangle with a perimeter of 30 cm and an area of 56 cm2. Which dimensions match Alice's rectangle?

The dimensions that match Alice's rectangle are 7 cm and 8 cm.

Step-by-step explanation:

The perimeter of the rectangle is given by:

   (1)                              

Where a and b are the sides of the rectangle

Also, the area of the rectangle is:

  (2)

By solving equation (1) for a, we have:

     (3)                      

Now, by entering equation (3) into (2) we can find one side of the rectangle:

Solving the above quadratic equation we have:

b₁ = 7 cm  and b₂ = 8 cm                      

Now, the other side of the rectangle can be calculated with equation (3):

or    

Taking the first solution (b₁) or the second (b₂), we find that the dimensions that match Alice's rectangle are 7 cm and 8 cm.          

Therefore, the dimensions that match Alice's rectangle are 7 cm and 8 cm.

I hope it helps you!                            

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step-by-step explanation:

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