Answer:
m=9 cm; n=4 cm
Step-by-step explanation:
The area of the rectangle is m*n, and the area of the square is 6*6. We are told that the areas of the rectangle and square equal each other, so:
[tex]m*n=36[/tex]
We are told that m is 5 cm longer than n, so we know that:
[tex]m = 5+n[/tex]
Therefore, we can solve for n using substitution.
[tex]m*n=36\\(5+n)n = 36\\5n+n^2 = 36\\n^2 + 5n -36 = 0\\(n+9)(n-4)=0[/tex]
We now have two answers for n: -9 and 4. However, the side length cannot be negative; that simply wouldn't make any sense. Therefore, n = 4.
Next, using the same equation, plug in 4 for n and solve for m.
[tex]m*n=36\\m*4=36\\m=9[/tex]
