Question

Please help me with this

Answer 1

m=9 cm; n=4 cm

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:

`m*n=36`

We are told that m is 5 cm longer than n, so we know that:

`m = 5+n`

Therefore, we can solve for n using substitution.

`m*n=36\\(5+n)n = 36\\5n+n^2 = 36\\n^2 + 5n -36 = 0\\(n+9)(n-4)=0`

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.

`m*n=36\\m*4=36\\m=9`