Its 2x^2-4x, to check it add it to 3x^2-2x or
2x^(2)-4x+3x^(2)-2x
Area of the three equally sized stripes: A
A=(x+15)(x)(3)
A=3x(x+15)
A=3x^2+45x
One gallon of paint will cover an area of no more than 400 square feet: <=400
She only has half of a gallon of paint left:
1/2(400 square feet)=400/2=200 square feet
Inequality that could be used to find the maximum height, in feet, of each stripe:
A<=200
3x^2+45x<=200
Answer: 3x^2+45x <= 200
Could her stripes be 3' tall?
x=3→A=3(3)^2+45(3)=3(9)+135=27+135→A=162<200 Ok
Yes, her stripes could be 3' tall.
Answer: Yes
Could her stripes be 4' tall?
x=4→A=3(4)^2+45(4)=3(16)+180=48+180→A=228>200 No
No, her stripes couldn't be 4' tall.
Answer: No
The answer is 4:15. (Also NEVER click on links with the bit . ly thing)
When you get to the point where the width is larger than the length, you can stop because you have exhausted all the possibilities. The greatest area will be the rectangle that is closer in to a square than any of the others.
