Question 187015
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Our calculations will be based on the assumption that one end of the ladder will rest on the top of the 15ft wall. The rest wil look like this:
{{{drawing(400,400,-1,6,-1,12,line(0,0,0,10),line(0,10,.2,10),line(.2,10,.2,0),line(.2,0,0,0),green(line(5,0,.2,10)),red(locate(2.5,5,L=ladder)),red(locate(2.2,-.1,x=distance)),red(locate(-.2,5,wall=15ft)),line(0,0,5,0))}}}--->Condition:{{{x/L=1/2}}}={{{L=2x}}}
That forms a Right Triangle, Pyth.Theorem remember?
{{{L^2=15^2+x^2}}}---> as per condtn:{{{L=2x}}}
{{{(2x)^2=225+x^2}}}
{{{4x^2=225+x^2}}}--->{{{4x^2-x^2=225}}}
{{{3x^2=225}}}---->{{{cross(3)x^2/cross(3)=cross(225)75/cross(3)}}}
{{{x=sqrt(75)=highlight(8.66ft)}}}, Distance from the Wall
Remember our condition:{{{x/L=1/2}}}
{{{8.66/L=1/2}}}--->{{{L=8.66*2=highlight(17.32ft)}}},Length of Ladder
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Let's check by going back to our Eqn:
{{{17.32^2=15^2+8.66^2}}}
{{{300ft^2=225ft^2+74.9956ft^2}}}
{{{300ft^2=300ft^2}}}, close enough, we round off.

Thank you,
Jojo</pre>