The larger leg of a right triangle is 3 cm longer than its smaller leg. the hypotenuse is 6 cm longer than the smaller leg. how many centimeters long is the smaller leg?

For rigt triangle with legs legnth a and b and hypotnuse legnth c

a^2+b^2=c^2

we are given
larger leg is 3 longer than smaller leg
hypotnuse is 6 longer than smaller
find smaller

ok so

first pick a smaller leg
lets say b is smaller
longer leg is 3 more than shorter leg
a is 3 more than b
a=3+b
and

hypontuse is 6 more than shorter
c=6+b

sub 3+b for a and 6+b for c in oroiginal equation'

a^2+b^2=c^2
(3+b)^2+b^2=(6+b)^2
9+6b+b^2+b^2=36+12b+b^2
2b^2+6b^2+9=b^2+12b+36
minus (b^2+12b+36) from both sides
b^2-6b-27=0
factor
(b-9)(b+3)=0
set equal to zero

b-9=0
b=9

b+3=0
b=-3
fasle, legnths cannot be negative

answer is shorter side=9 cm