a, b, and c are the legs
one is 5 longer than other
a=5+b
if hypothuse is 25 then c=25
remember, if the legs are a and b and the hypothuse is length c then
[tex]a^2+b^2=c^2[/tex]
so
wait, a=5+b so subsitute 5+b for a
[tex](5+b)^2+b^2=25^2[/tex]
[tex]b^2+10b+25+b^2=625[/tex]
[tex]2b^2+10b+25=625[/tex]
minus 625 from both sides
[tex]2b^2+10b-600=0[/tex]
factor out the 2
[tex]2(b^2+5b-300)=0[/tex]
what 2 numbers multiply to get -300 and add to get 5?
20 and -15
[tex]2(b+20)(b-15)=0[/tex]
set to zero
b+20=0
b=-20
false, can't have negative length of leg
b-15=0
b=15
b=15
a=5+b
a=5+15
a=20
the lengths of the legs are 20in and 25in
