document.write( "Question 138911: This question is a word problem using the quadratic formula A rectangular poool has dimensions of 40 ft and 60 ft. If the pool has a patio area around it that equals the area of the pool, how wide is the distance from the pool edge to the patio edge. \n" ); document.write( "
Algebra.Com's Answer #101404 by ankor@dixie-net.com(22740)![]() ![]() You can put this solution on YOUR website! This question is a word problem using the quadratic formula A rectangular pool has dimensions of 40 ft and 60 ft. If the pool has a patio area around it that equals the area of the pool, how wide is the distance from the pool edge to the patio edge. \n" ); document.write( ": \n" ); document.write( "Let x = the width of the patio around the pool \n" ); document.write( ": \n" ); document.write( "The dimension of the pool and the patio: \n" ); document.write( "(2x+40) by (2x+60) \n" ); document.write( ": \n" ); document.write( "Area of the pool 40*60 = 2400 q/ft, Total area of both: 4800 sq/ft \n" ); document.write( ": \n" ); document.write( "Total Area equation: \n" ); document.write( "(2x+40)(2x+60) = 4800 \n" ); document.write( "FOIL \n" ); document.write( "4x^2 + 200x + 2400 = 4800 \n" ); document.write( ": \n" ); document.write( "4x^2 + 200x + 2400 - 4800 = 0 \n" ); document.write( ": \n" ); document.write( "4x^2 + 200x - 2400 = 0 \n" ); document.write( ": \n" ); document.write( "Simplify, divide by 4; \n" ); document.write( "x^2 + 50x - 600 = 0 \n" ); document.write( ": \n" ); document.write( "Factor: \n" ); document.write( "(x+60)(x-10) = 0 \n" ); document.write( ": \n" ); document.write( "The positive solution: \n" ); document.write( "x = 10 ft is the width of the patio \n" ); document.write( "; \n" ); document.write( "Check solution by finding the total area: (40+20) * (60+20) = 4800 \n" ); document.write( ": \n" ); document.write( "You can use the quadratic formula if you wish: a=1, b=50, c=-600 \n" ); document.write( " |