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