I can't understand this problem, the answers don't seem to fit with the context.
The problem gave us the area of the picture, the length and width of the picture, and the area of the frame, but not the length or width of the frame. I know that part of the measurement of the width is equal to five and that part of the measurement of the length is nine.
I set each corner equal to x and then I created the following equations, 2x +5 is my width and 2x+9 is my length, I multiplied x by 2 because two corners make up part of my width measurement. Then, I did my area formula by multiplying these two equations and set them equal too 90, which is the area of the total picture and the frame.
Then I created a quadratic equation by subtracting 90 from both sides, and multiplying my equations.
This gave me 4x^2 + 28x -45. Using the foil method, I tried to factor the equation but found it impossible too do so. I couldn't find any values for x that would make my frame area equal to 45.
Then, I tried just solving 2x + 5 and 2x + 9 equal too 0 but these gave me negative answers of -2.5 and -4.5, and frame measurements cannot be equal too 0. Thus, I think this problem cannot be solved.