document.write( "Question 830276: There are two circular gardens A and B.The circumference of garden A is 1.760Km and the area of garden B is 25 times the area of garden A. find the circumference of garden B. \n" ); document.write( "
Algebra.Com's Answer #500553 by math-vortex(648)\"\" \"About 
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document.write( "Hi, there--\r\n" );
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document.write( "THE PROBLEM:\r\n" );
document.write( "There are two circular gardens A and B.The circumference of garden A is 1.760Km and the \r\n" );
document.write( "area of garden B is 25 times the area of garden A. Find the circumference of garden B.\r\n" );
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document.write( "A SOLUTION:\r\n" );
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document.write( "I can think of several ways to solve this problem: a long way and a short way. Here's the \r\n" );
document.write( "LONG WAY first…\r\n" );
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document.write( "We know the circumference of Garden A. We can work backwards to find the area of garden A.\r\n" );
document.write( "The formula for the circumference C of a circle with radius r is\r\n" );
document.write( "\"C=2%2Api%2Ar\"\r\n" );
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document.write( "Substitute 1.760 for C and solve for r.\r\n" );
document.write( "\"1.760=2%2Api%2Ar\"\r\n" );
document.write( "\"r=1.760%2F%282%2Api%29\"\r\n" );
document.write( "\"r=0.880%2Fpi\"\r\n" );
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document.write( "The radius of garden A is \"0.880%2Fpi\" km. We won't give an approximation for \"pi\" until \r\n" );
document.write( "the final step of the problem.)\r\n" );
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document.write( "Given the radius, we can work backwards to find the area of garden A. The formula for the\r\n" );
document.write( "area of a circle with radius r is\r\n" );
document.write( "\"A=pi%2Ar%5E2\"\r\n" );
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document.write( "Substitute \"0.880%2Fpi\" for r and solve for S.\r\n" );
document.write( "\"A=pi%2A%280.880%2Fpi%29%5E2\"\r\n" );
document.write( "\"A=pi%2A%280.7744%2F%28pi%29%5E2%29\"\r\n" );
document.write( "\"A=0.7744%2Fpi\"\r\n" );
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document.write( "The area of garden B is 25 times the area of garden A. To find the area of garden B, multiply\r\n" );
document.write( "the area of garden A by 25. \r\n" );
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document.write( "\"%280.7744%2Fpi%29%2A25=19.36%2Fpi\"\r\n" );
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document.write( "The area of Garden B is \"19.36%2Fpi\" square km. We can work backwards to find the radius. \r\n" );
document.write( "Substitute \"19.36%2Fpi\" for A and solve for r.\r\n" );
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document.write( "\"A=pi%2Ar%5E2\"\r\n" );
document.write( "\"19.36%2Fpi=pi%2Ar%5E2\"\r\n" );
document.write( "\"r%5E2=19.36%2F%28pi%29%5E2\"\r\n" );
document.write( "\"r+=4.4%2Fpi\"\r\n" );
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document.write( "Given the radius of Garden B, we can determine its circumference. Substitute \"4.4%2Fpi\" for r \r\n" );
document.write( "and simplify.\r\n" );
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document.write( "\"C=2%2Api%2Ar\"\r\n" );
document.write( "\"C=2%2Api%2A%284.4%2Fpi%29\"\r\n" );
document.write( "\"C=8.8\"\r\n" );
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document.write( "The circumference of Garden B is 8.8 km.\r\n" );
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document.write( "THE SHORTER WAY:\r\n" );
document.write( "Because the gardens are both circles, we know that they are similar figures.\r\n" );
document.write( "The circumferences of the two circles will vary by some factor, and the areas will vary by the square of that factor. \r\n" );
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document.write( "We are given that the areas of the circles vary by a factor of 25. Therefore, the circumferences\r\n" );
document.write( "will vary by a factor of \"sqrt%2825%29=5\". In other words, the circumference of B is 5 times the \r\n" );
document.write( "circumference of A.\r\n" );
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document.write( "The circumference of garden B is (5)(1.760)=8.8 km. The LONG WAY is actually a proof that\r\n" );
document.write( "this SHORT WAY works. Never do more work than you have to. Let the math do the work for \r\n" );
document.write( "you!!!\r\n" );
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document.write( "Hope this helps! Feel free to email if you have any questions about the solution.\r\n" );
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document.write( "Good luck with your math,\r\n" );
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document.write( "Mrs. F\r\n" );
document.write( "math.in.the.vortex@gmail.com\r\n" );
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