Carla’s kitchen floor is in the shape of a perfect square. Her copycat brother, Carl, wants to re-model his kitchen so that it will have the same surface area as his sister, but his kitchen will be rectangular. The length of his floor is half the length of his sister’s, plus 10 feet. The width of his floor will be 2 feet smaller than half the length of his sister’s. Show your analysis as you determine the dimensions of the 2 kitchen floors.
I have set mine up to be n^2=(1/2n+10)(1/2n-2)
Which leaves me with 0=.75n+4n-20. But I'm not sure what to do?
I'd say just solve for n. But looking here
http://www.wolframalpha.com/input/?i=n^2%3D%281%2F2n%2B10%29%281%2F2n-2%29
it appears there is no solution. A typo in the problem?
To solve the equation 0 = 0.75n + 4n - 20, you can simplify and combine like terms on the right-hand side of the equation:
0 = 0.75n + 4n - 20
0 = 4.75n - 20
Next, isolate the term with n by adding 20 to both sides of the equation:
20 = 4.75n
To solve for n, divide both sides of the equation by 4.75:
20 / 4.75 = n
This gives you the value of n:
n ≈ 4.21
Since n represents the length of the kitchen floor, you now have an approximate value for the length of Carla's kitchen floor.
To find the dimensions of the kitchen floors, you can use the given relationships:
Length of Carl's floor = 1/2 * length of Carla's floor + 10
Width of Carl's floor = 1/2 * length of Carla's floor - 2
Substituting the value of n into these relationships:
Length of Carl's floor ≈ 1/2 * 4.21 + 10 ≈ 12.11 feet
Width of Carl's floor ≈ 1/2 * 4.21 - 2 ≈ 0.61 feet
Therefore, the approximate dimensions of Carla's kitchen floor are 4.21 feet by 4.21 feet, while the approximate dimensions of Carl's kitchen floor are 12.11 feet by 0.61 feet.