Respuesta :
Answer:
1.5 inches.
Step-by-step explanation:
Let x represent width of the frame.
We have been given that Mikaela places a frame around a print that measures 10 inches by 10 inches. The area of just the frame itself is 69 square inches.
The area of the print would be [tex]10\times 10=100[/tex] square inches.
The side of frame with print would be [tex]10+x+x=10+2x[/tex] because the width will be on both sides.
Area of side of frame with print would be [tex](10+2x)^2[/tex].
Area of the frame will be equal to area of side of frame with print minus area of print.
We can represent this information in an equation as:
[tex]69=(10+2x)^2-100[/tex]
Let us solve for x.
[tex]69+100=(10+2x)^2-100+100[/tex]
[tex]169=(10+2x)^2[/tex]
[tex](10+2x)^2=169[/tex]
Take square root of both sides:
[tex]\sqrt{(10+2x)^2}=\pm\sqrt{169}[/tex]
[tex]10+2x=\pm 13[/tex]
[tex]10+2x=- 13\text{ (or) } 10+2x=13[/tex]
[tex]2x=- 23\text{ (or) } 2x=3[/tex]
[tex]x=-\frac{ 23}{2}\text{ (or) } x=\frac{3}{2}[/tex]
[tex]x=-11.5\text{ (or) } x=1.5[/tex]
Since width cannot be negative, therefore, width of the frame is 1.5 inches.
