SOLUTION: Model with a quadratic equation, then solve. Find the dimensions of a square picture that make the area of the picture equal to 75% of the total area enclosed by the frame. The t

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: Model with a quadratic equation, then solve. Find the dimensions of a square picture that make the area of the picture equal to 75% of the total area enclosed by the frame. The t      Log On


   

Question 568702: Model with a quadratic equation, then solve.
Find the dimensions of a square picture that make the area of the picture equal to 75% of the total area enclosed by the frame. The total length of the side is 12inches, including the frame.
I thought y=axsquared for the equation
144=0.75x2
192=x2
x=13.9 But this is larger than the length of the picture frame???
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
You've got it backwards.
If the length of the side of the picture frame is 12 inches, the total area of frame plus picture is
12%5E2 square inches = 144 square inches.
If x inches is the length of the side of the square picture, the area of the square picture is x%5E2 square inches. Since that is 75% of the 144 square inches of total area,
x%5E2=0.75%2A144 --> x%5E2=108
Solving:
x=sqrt%28108%29 --> x=sqrt%284%2A27%29 --> x=sqrt%282%5E2%2A3%5E3%29 --> x=sqrt%282%5E2%29%2Asqrt%283%5E3%29 --> x=sqrt%282%5E2%29%2Asqrt%283%5E2%2A3%29 --> x=2%2Asqrt%283%5E2%29%2Asqrt%283%29 --> x=2%2A3%2Asqrt%283%29 --> x=6sqrt%283%29