Question 227769
Problem 1.  A SQUARE AND RECTANGLE HAVE EQUAL AREAS. IF THE RECTANGLE IS 36 BY 16, WHAT IS THE SIDE OF A SQUARE?


Step 1.  The area of a rectangle A=36*16=576 (area=base*height}}}


Step 2.  The square has equal sides where we let s be the side which is equal to the base and height so A=s*s=s^2.


Step 3.  The areas are equal in Steps 1 and 2.  Then {{{s^2=576}}}


Step 4.  Take the square root to both sides of the equation or {{{s=24}}}.


Step 5.  ANSWER:  The side of the square is 24.


Problem 2.  IN A SOCIAL HALL OF A BUILDING, THERE ARE 150 SEATS ARRANGED IN ROWS WITH 5 MORE SEATS PER ROW THAN THE NUMBER OF ROWS. HOW MANY SEATS ARE THERE IN EACH ROW?


Step 1.  Let n be the number of rows.


Step 2.  Let n+5 be the number of  seats per row.


Step 3.  Then, n(n+5)=150 since there are 150 seats.


Step 4.  Subtract 150 to both sides of equation in Step 3.


{{{n^2+5n-150=150+150}}}


{{{n^2+5n-150=0}}}


Step 5.  To solve, use the quadratic equation given as


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


where a=1, b=5, and c=-150


*[invoke quadratic "n", 1, 5, -150 ]


Selecting the positive solution of {{{n=10}}} and {{{n+5=15}}} and note the product is 150 seats.


Step 6. ANSWER:  The number of seats in each row is 15 seats.


I hope the above steps were helpful.


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And good luck in your studies!


Respectfully,
Dr J

http://www.FreedomUniversity.TV