SOLUTION: 9. A picture frame has thickness x, and the dimensions of the unframed picture are 18in x 24in. If the area of the picture and frame together is 720 square inches, find the thickn

Algebra ->  Customizable Word Problem Solvers  -> Geometry -> SOLUTION: 9. A picture frame has thickness x, and the dimensions of the unframed picture are 18in x 24in. If the area of the picture and frame together is 720 square inches, find the thickn      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 945726: 9. A picture frame has thickness x, and the dimensions of the unframed picture are 18in x 24in. If the area of the picture and frame together is 720 square inches, find the thickness of the frame.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
The area of the picture plus the frame is:
+%28+x+%2B+18+%29%2A%28+x+%2B+24+%29+=+720+ in2
+x%5E2+%2B+18x+%2B+24x+%2B+432+=+720+
+x%5E2+%2B+42x+-+288+=+0+
Use quadratic equation
+x+=+%28+-b+%2B-+sqrt%28+b%5E2+-+4%2Aa%2Ac+%29%29+%2F+%282%2Aa%29+
+a+=+1+
+b+=+42+
+c+=+-288+
+x+=+%28+-42+%2B-+sqrt%28+42%5E2+-+4%2A1%2A%28-288%29+%29%29+%2F+%282%2A1%29+
+x+=+%28+-42+%2B-+sqrt%28+1764+%2B+1152+%29%29+%2F+2+
+x+=+%28+-42+%2B-+sqrt%28+2916+%29%29+%2F+2+
+x+=+%28+-42+%2B+54+%29+%2F+2+
+x+=+12%2F2+
+x+=+6+
The frame is 6 in wide
check:
+%28+x+%2B+18+%29%2A%28+x+%2B+24+%29+=+720+
+%28+6+%2B+18+%29%2A%28+6+%2B+24+%29+=+720+
+24%2A30+=+720+
+720+=+720+
OK