Question

the hypotenuse of a right triangle is 3m more than twice the short leg. the longer leg is 2m more than twice the shorter leg. find the lengths of the sides?

Answer 1

s=short leg
h=hypotenuse
l=other leg
h=3+2s
l=2+2s
right triangle use Pythagorean thm
so h^2=l^2+s^2
(3+2s)^2=(2+2s)^2+s^2
solve for s

Answer 2

9+2*3*2s+4s^2=4+2*2*2s+4s^2+s^2
9+12s+4s^2=4+8s+4s^2+s^2
4s^2-4s^2-s^2+12s-8s+9-4=0
-s^2+4s+5=0
s^2-4s-5=0
(s-5)(s+1)=0
s=5
s=-1

Answer 3

but a leg cannot have length -1
so s=5 is the shorter leg
if s=5, then h=3+2(5)=13 and l=2+2(5)=12
we can check
h^2=s^2+l^2
does it?
13^2=5^2+12^2
169=25+144
169=169
so done!
everything checks out!

Answer 4

thank you lots =]