#### Answer

(3,4) or (4,3)

#### Work Step by Step

Given The perimeter of a right triangle is 12 m. If the hypotenuse has a length of 5 m, We need to find the lengths of the two legs.
Lets assume that the right triangle legs are a and b
Perimeter = a+b+ hypotenus
12 = a+b + 5
a+b = 7m
By pythagoras theorem
$hypotenus^{2}$ =$a^{2}$ + $b^{2}$
$5^{2}$ = $(b-7)^{2}$ + $b^{2}$
25 = $b^{2}$ + 49 -14b + $b^{2}$
25 = 2$b^{2}$ +49 -14b
2$b^{2}$ +24 - 14b = 0
$b^{2}$ - 7b + 12= 0
$b^{2}$ -3b -4b +12 = 0
b(b-3) - 4(b-3) = 0
(b-4)(b-3) = 0
(b-4) =0, (b-3) = 0
So, b =4,3
Now use the value of b in a+b = 7m
a+4=7
a =3
or
a+3=7
a=4
So legs of the right triangle be(3,4)(4,3)