SOLUTION: The length and width of an 8cm X 12cm photograph are increased by the same amount in order to double its area. What are the new dimensions?

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Question 1051152: The length and width of an 8cm X 12cm photograph are increased by the same amount in order to double its area. What are the new dimensions?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +A+ = the original area
+A+=+8%2A12+
+A+=+96+
+2A+=+192+
-----------------
+%28+8+%2B+x+%29%2A%28+12+%2B+x+%29+=+192+
+96+%2B+12x+%2B+8x+%2B+x%5E2++=+192+
+x%5E2+%2B+20x+=+96+
Complete the square
+x%5E2+%2B+20x+%2B+%28+20%2F2+%29%5E2+=+96+%2B+%28+20%2F2+%29%5E2+
+x%5E2+%2B+20x+%2B+100+=++196+
+%28+x+%2B+10+%29%5E2+=+14%5E2+
+x+%2B+10+=+14+
+x+=+4+
----------------
+8+%2B+x+=+12+
+12+%2B+x+=+16+
The new dimensions are 12 x 16
---------------
check:
+8%2A12+=+96+
and
+12%2A16+=+192+
+2%2A96+=+192+
OK