Answer:
The dimensions of the frame are 15 in x 13 in
Step-by-step explanation:
Let
x ----> the length of the picture
y ----> the width of the picture
we know that
[tex]x=2+y[/tex] -----> equation A
The area of the picture, including the frame is
[tex]A=(x+6)(y+6)[/tex]
[tex]A=195\ in^2[/tex]
so
[tex]195=(x+6)(y+6)[/tex] ----> equation B
substitute equation A in equation B
[tex]195=(2+y+6)(y+6)[/tex]
solve for y
[tex]195=(y+8)(y+6)\\y^2+6y+8y+48=195\\\\y^2+14y-147=0[/tex]
solve the quadratic equation by graphing
The solution is y=7 in
see the attached figure
Find the value of x
[tex]x=2+7=9\ in[/tex]
Find the dimensions of the frame
[tex]x+6=9+6=15\ in[/tex]
[tex]y+6=7+6=13\ in[/tex]
therefore
The dimensions of the frame are 15 in x 13 in
