Bradley T. answered • 01/20/23
Tutor
5
(4)
Tutor for Python and High School and Middle School Math
The area of a rectangle is length times width. We are given a quadratic equation. We want to find two things, two expressions, that when multiplied together make this quadratic. Factoring it should give us this. This problem is a factoring problem wrapped with some extra words to make it a word problem.
You can use any factoring method you like. A quick summary:
- Notice B. it is -8, this is a negative, but both a and c are positive. This means that our factors for c will be two negatives.
- Notice c = 1. This is very good for us, because the only factors of 1 is 1. But remember, b is negative. So our factor is made negative . Just to check, -1 x -1 = 1.
- The factors of 16: 1 and 16 , 2 and 8, 4 and itself. We want to multiple these factors by our c factors then add them and we want them to equal B. We want this to equal -8
- (-1 x 1 ) + (-1x16) = -17 NOT -8
- (-1 x 2) + (-1x8)= -10 NOT -8
- (-1 x 4) + (-1 x 4) = -8 That's what we want
- Our factors: (4x-1)(4x-1)
Both the length and width is 4x-1
Bradley T.
I agree, the problem could be better worded. I don't believe I made the assumption of the rectangle being a square though. I just factored the quadratic which just so happened to be a perfect square in this case.
Report
01/20/23
Meira P.
Square is the only possible real solution for this problem.
Report
01/21/23
Mark M.
Your solution, although correct, is based on the assumption that the rectangle in the problem is a square. The problem can be faulted for being poorly posed.01/20/23