A picture inside a frame is 2 inches longer than it is wide. The picture is in a frame that has a width of 3 inches on each side of the picture. If the area of the picture, including the frame, is 195 inches^2, find the dimensions of the frame.
Accepted Solution
A:
Answer:The dimensions of the frame are 15 in x 13 inStep-by-step explanation:Letx ----> the length of the picturey ----> the width of the picturewe know that[tex]x=2+y[/tex] -----> equation AThe 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 Bsubstitute 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 graphingThe solution is y=7 insee the attached figureFind 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]thereforeThe dimensions of the frame are 15 in x 13 in