given:
foot of laddder=base=b=10ft
length of ladder=hypotenuse=[tex]l[/tex]=?
height of wall=altitude=x=[tex]l[/tex]-2 =? (according to condition)
calculation:
by using Pythagoras theorem
[tex](hypotenus)^{2}[/tex]=[tex](altitude)^{2}[/tex]+[tex](base)^{2}[/tex]
⇒ [tex]l^{2}[/tex]=[tex](l-2)^{2}[/tex]+[tex](10)^{2}[/tex]
⇒ [tex]l^{2}[/tex]= [tex]l^{2}[/tex]-4[tex]l[/tex]+100
⇒ [tex]4l=104[/tex]
⇒ [tex]l[/tex]=26ft
also x=[tex]l[/tex]-2=26-2=24ft
checking:
putting the obtained values in Pythagoras theorem
⇒ [tex](26)^{2}=(24) ^{2} +(10)^{2}[/tex]
⇒ 676=100+576
⇒ 676=676
hence the given solution is correct.
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