a frame painting has an overall dimension of 32" x 29"
area of painting alone is 550 square inches. what is the width of frame??
+36916 Square area of the whole framed picture = 32 x 29 = 928 in^2
928-550 = 378 in^2 = area of frame
32 x 29 -( (32-x) (29-x)) = area of frame= 378 in^2 where x = 2 times the width of the frame
928 - x^2 + 61x - 928 = 378
-x^2+61x-378 = 0 Use Quadratic Formula to find x = 54 or 7 (54 is too big...toss it out)
x = 7 width = 1/2 x = 3.5 inches
As a check....does the inside dimension of the frame = the picture size of 550 in^2 ?
(32-7)(29-7) = 550 Check!
+36916 Square area of the whole framed picture = 32 x 29 = 928 in^2
928-550 = 378 in^2 = area of frame
32 x 29 -( (32-x) (29-x)) = area of frame= 378 in^2 where x = 2 times the width of the frame
928 - x^2 + 61x - 928 = 378
-x^2+61x-378 = 0 Use Quadratic Formula to find x = 54 or 7 (54 is too big...toss it out)
x = 7 width = 1/2 x = 3.5 inches
As a check....does the inside dimension of the frame = the picture size of 550 in^2 ?
(32-7)(29-7) = 550 Check!
