SOLUTION: A rectangular photo of dimensions 8 inches by 9 inches is place in a picture frame of uniform width of all sides. The resulting total area ( both picture and frame)is 156 square in

Algebra ->  Vectors -> SOLUTION: A rectangular photo of dimensions 8 inches by 9 inches is place in a picture frame of uniform width of all sides. The resulting total area ( both picture and frame)is 156 square in      Log On


   

Question 833254: A rectangular photo of dimensions 8 inches by 9 inches is place in a picture frame of uniform width of all sides. The resulting total area ( both picture and frame)is 156 square inches.
What is the width of the picture frame?
Set up and solve an equation to answer this problem.

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let the width of the frame = +w+
+2w+ gets added to each side of the photo
+%28+8+%2B+2w+%29%2A%28+9+%2B+2w+%29+=+156+
+72+%2B+18w+%2B+16w+%2B+4w%5E2+=+156+
+4w%5E2+%2B+34w+-+84+=+0+
+2w%5E2+%2B+17w+-+42+=+0+
Use the quadratic formula
+w+=+%28+-b+%2B-+sqrt%28+b%5E2+-+4%2Aa%2Ac+%29%29+%2F+%282%2Aa%29+
+a+=+2+
+b+=+17+
+c+=+-42+
+w+=+%28+-17+%2B-+sqrt%28+17%5E2+-+4%2A2%2A%28-42%29+%29%29+%2F+%282%2A2%29+
+w+=+%28+-17+%2B-+sqrt%28+289+%2B+336+%29%29+%2F+4+
+w+=+%28+-17+%2B-+sqrt%28+625+%29%29+%2F+4+
+w+=+%28+-17+%2B+25+%29+%2F+4+ ( I can't use the minus square root )
+w+=+8%2F4+
+w+=+2+
The width of the frame is 2 in
check:
+%28+8+%2B+2w+%29%2A%28+9+%2B+2w+%29+=+156+
+%28+8+%2B+2%2A2+%29%2A%28+9+%2B+2%2A2+%29+=+156+
+%28+8+%2B+4+%29%2A%28+9+%2B+4+%29+=+156+
+12%2A13+=+156+
+156+=+156+
OK