SOLUTION: 2 different rectangles have the same width. All four sides of both rectangles have integer lengths.The areas of the rectangles are 1086 and 828. Find the largest possible value of

Algebra ->  Equations -> SOLUTION: 2 different rectangles have the same width. All four sides of both rectangles have integer lengths.The areas of the rectangles are 1086 and 828. Find the largest possible value of      Log On


   

Question 67859: 2 different rectangles have the same width. All four sides of both rectangles
have integer lengths.The areas of the rectangles are 1086 and 828. Find the largest possible value of the common width of the rectangles?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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2 different rectangles have the same width. All four sides of both rectangles
have integer lengths. The areas of the rectangles are 1086 and 828. Find the largest possible value of the common width of the rectangles?
:
Since all dimensions are integers, it makes sense to prime factor the areas:
:
1086 = 2 * 3 * 181
:
828 = 2 * 2 * 3 * 3 * 23
:
The highest common factor is 3
:
The width is 3,
:
Large rectangle length: 1086/3 = 362
:
Small rectangle length: 828/3 = 276