Answer:
[tex]4x^2+14x-3=0[/tex]
Step-by-step explanation:
We have been given that the mirror is 3 feet wide and the thickness of the frame is x, so width of the frame would be [tex]x+x=2x[/tex].
The width of mirror with frame would be [tex]2x+3[/tex].
Similarly, the length of the frame would be [tex]x+x=2x[/tex] and the length of mirror with frame would be [tex]2x+4[/tex].
We know that area of rectangle is width times length, so area of frame with mirror would be [tex](2x+3)(2x+4)[/tex].
We are told that The mirror and frame must have an area of 15 square feet, so we can equate our equation with 15 as:
[tex](2x+3)(2x+4)=15[/tex]
Upon simplifying our equation, we will get:
[tex]4x^2+8x+6x+12=15[/tex]
[tex]4x^2+14x+12=15[/tex]
[tex]4x^2+14x+12-15=15-15[/tex]
[tex]4x^2+14x-3=0[/tex]
Therefore, our required equation would be [tex]4x^2+14x-3=0[/tex].
