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