SOLUTION: Janeel has a 10 inch by 12 inch photograph. She wants to scan the photograph, then reduce the results by the same amount in each dimension to post on her Web site. Janeel wants the

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Janeel has a 10 inch by 12 inch photograph. She wants to scan the photograph, then reduce the results by the same amount in each dimension to post on her Web site. Janeel wants the      Log On


   

Question 716803: Janeel has a 10 inch by 12 inch photograph. She wants to scan the photograph, then reduce the results by the same amount in each dimension to post on her Web site. Janeel wants the area of the image to be one eight of the original photograph. Write an equation to represent the area of the reduced image. Find the dimensions of the reduced image.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let the amount that she wants to reduce each
dimension by = +x+
The new dimensions will be
+10+-+x+ by +12+-+x+
The area of the new image is to be
+%28+10%2A12+%29+%2F+8+
+120%2F8+=+%28+10+-+x+%29%2A%28+12+-+x+%29+
+15+=+120+-+12x+-+10x+%2B+x%5E2+
+x%5E2+-22x+%2B+105+=+0+
Use the quadratic formula
+x+=+%28-b+%2B-+sqrt%28+b%5E2+-+4%2Aa%2Ac+%29%29+%2F+%282%2Aa%29+
+a+=+1+
+b+=+-22+
+c+=+105+
+x+=+%28-%28-22%29+%2B-+sqrt%28+%28-22%29%5E2+-+4%2A1%2A105%29%29+%2F+%282%2A1%29+
+x+=+%28+22+%2B-+sqrt%28+484+-+420%29%29+%2F+2+
+x+=+%28+22+%2B-+sqrt%28+64%29%29+%2F+2+
+x+=+%28+22+%2B+8+%29+%2F+2+
+x+=+15+
This is bigger than the starting dimensions, so I can't use this result
+x+=+%28+22+-+8+%29+%2F+2+
+x+=+14%2F2+
+x+=+7+ This can work
check:
+120%2F8+=+%28+10+-+x+%29%2A%28+12+-+x+%29+
+15+=+%28+10+-+7+%29%2A%28+12+-+7+%29+
+15+=+3%2A5+
+15+=+15+
OK
The dimensions of the reduced image are 3 x 5