Question 214941
The length of each side of a square is increased by 4 in. The sum of the areas of the original square and the larger square is 106 in^2. What is the length of a side of the original square?


Step 1.  Let s be the length of the side of the original square then Area A of a square is {{{A=s^2}}}.


Step 2.  {{{(s+4)^2}}}  Area of square with side increased by 4.


Step 3.  Then using the problem statement where the sum of the areas of the two squares is 106 square inches, we have


{{{s^2+(s+4)^2=106}}} 


{{2{s^2+8s+16=106}}}


Step 4.  Subtract 106 from both sides to get a quadratic equation


{{{2s^2+8s+16-106=106-106}}}


{{{2s^2+8s-90=0}}}


Step 5.  We can now use the quadratic formula to solve this equation given as


{{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}}


where a=2, b=8 and c=-90


*[invoke quadratic "s", 2, 8, -90 ]


Select the positive solution of s=5.  


As a check, {{{s^2+(s+4)^2= 25+81=106}}}.  So it works!


Step 6.  The length of the original square is 5 inches.


I hope the above steps were helpful.


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Good luck in your studies!


Respectfully,
Dr J