Question 178137
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Let's see the rectangular patio:
{{{drawing(300,300,-5,5,-1,5,line(-4,0,-4,3),blue(line(-4,3,4,3)),blue(line(4,3,4,0)),line(4,0,-4,0),blue(line(-4,3,4,0)),locate(-.5,3,7+x),locate(4.2,1.5,x),locate(-.2,1.9,13ft),green(line(3.7,3,3.7,2.7)),green(line(3.7,2.7,4,2.7)))}}}
It forms a Right Triangle. Then by Pyth.Theorem:
{{{13^2=(x+7)^2+x^2}}}------------> Working eqn
{{{x^2+14x+49+x^2-169=0}}}
{{{2x^2+14x-120=0}}}
where{{{system(a=2,b=14,c=-120)}}}
{{{x=(-b+-sqrt(b^2-4ac))/2a=(-14+-sqrt(14^2-4*2*-120))/(2*2)}}}
{{{x=(-14+-sqrt(196+960))/4=(-14+-sqrt(1156))/4=(-14+-34)/4}}}
2 values:
{{{x=(-14-34)/4=-48/4=-12}}}, discard
{{{x=(-14+34)/4=20/4=highlight(5ft)}}}, WIDTH
{{{5+7=highlight(12ft)}}}, LENGTH
In doubt? Go back Working eqn:
{{{13^2=5^2+12^2}}}
{{{169=25+144}}}
{{{169ft=169ft}}}----->{{{drawing(300,300,-5,5.5,-1,5,line(-4,0,-4,3),blue(line(-4,3,4,3)),blue(line(4,3,4,0)),line(4,0,-4,0),blue(line(-4,3,4,0)),red(locate(-.5,3,12feet)),red(locate(4.2,1.5,5feet)),locate(-.2,1.9,13ft),green(line(3.7,3,3.7,2.7)),green(line(3.7,2.7,4,2.7)))}}}

Thank you,
Jojo</pre>