SOLUTION: Hi The total perimeter of two squares of different sizes is 68cm. The total area of both squares 157 cm squared. What is the length of the bigger square. Thanks

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Question 1175842: Hi
The total perimeter of two squares of different sizes is 68cm. The total area of both squares 157 cm squared. What is the length of the bigger square.
Thanks
Answer by math_helper(2461) About Me  (Show Source):
You can put this solution on YOUR website!
+highlight%2811cm%29

The workout:
Let s%5B1%5D and s%5B2%5D be the side lengths of the two squares

Start with two equations
+4s%5B1%5D+%2B+4s%5B2%5D+=+68+ ---> +s%5B1%5D+%2B+s%5B2%5D+=+17+
+s%5B1%5D%5E2+%2B+s%5B2%5D%5E2+=+157+

From here, substitute s%5B1%5D+=+17-s%5B2%5D from the top eqn into the bottom:
+%2817-s%5B2%5D%29%5E2+%2B+s%5B2%5D%5E2+=+157+
Simplify, and factor
+2s%5B2%5D%5E2+-34s%5B2%5D+%2B+132+=+0+
+s%5B2%5D%5E2+-+17s%5B2%5D+%2B+66+=+0+
+%28s%5B2%5D-11%29%28s%5B2%5D-6%29+=+0+
So +s%5B2%5D+=+11+ --> +s%5B1%5D+=+6+
or +s%5B2%5D+=+6+ --> +s%5B1%5D+=+11 <<< same answer, s%5B1%5D is simply the larger square for this solution
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Check: 4*11 + 4*6 = 44 + 24 = 68
11^2 + 6^2 = 121 + 36 = 157