Question 287667: COMPARING AREAS
A WIRE 390 IN. LONG IS CUT INTO TWO PIECES. ONE PIECE IS FORMED INTO A SQUARE. THE OTHER PIECE IS FORMED INTO A CIRCLE. IF THE TWO FIGURES HAVE THE SAME AREA, WHAT ARE THE LENGTHS OF THE TWO PIECES OF WIRE (TO THE NEAREST TENTH OF AN IN.)
THANKS.
Answer by CharlesG2(834)   (Show Source):
You can put this solution on YOUR website! COMPARING AREAS
A WIRE 390 IN. LONG IS CUT INTO TWO PIECES. ONE PIECE IS FORMED INTO A SQUARE. THE OTHER PIECE IS FORMED INTO A CIRCLE. IF THE TWO FIGURES HAVE THE SAME AREA, WHAT ARE THE LENGTHS OF THE TWO PIECES OF WIRE (TO THE NEAREST TENTH OF AN IN.)
THANKS.
will do this , but please in future avoid capital letters, okay? it's like shouting
area square = side^2
area circle = pi*r^2 (r being radius)
if areas equal then side = r*sqrt(pi)
perimeter square = 4 * side = 4*r*sqrt(pi)
perimeter circle = 2*r*pi
390 = 4*r*sqrt(pi) + 2*r*pi (and then need to solve for r)
390 = r * (4*sqrt(pi) + 2*pi)
390 = r * (7.08981540362206410919266993336458 + 6.28318530717958647692528676655901)
390 = r * (13.3730007108016505861179566999236)
29.1632378128110690359981779219183 = r (now calculate perimeters)
perimeter square = 206.761972664761351531516548842056
perimeter circle = 183.238027335238648468483451157944
perimeter square approx. 206.8 inches
perimeter circle approx. 183.2 inches
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