So

a^2+b^2=c^2

c=hypotenuse

a^2+b^2=20^2=400

if the permiter is 42 then

p=hypotonuse+side+side

42=20+side+side

subtract 20 from both sides

22=side+side

a+b=22

subtract b from both sides

a=22-b

subsitute for a in equation below

a+2+b^2=c^2

(22-b)^2+b^2=400

b^2-44x+484+b^2=400

2b^2-44x+484=400

divide both sides by 2

b^2-22x+242=200

subtract 200 from both sides

b^2-22x+42=0

factor

(b+/-number)(b+/-number)

to find the numbers, find which 2 number multiply to 42 and add to get -22

the numbers must be neative since same signs multiplied=positive and negative+negative=negative

(b-number)(b-number)

facrors of 42=2,3,6,7,14,21

2,21

3,14

6,7

itâ€™s hard to find the number, but the numbers are -19.8882 and -2.11181

(b-19.8882)(b-2.11181)=0

if xy=0 then assume that x and y=0

b-19.8882=0

add 19.8882 to both sides

b=19.8882

b-2.11181=0

add 2.11181 to both sides

b=2.11181

the side legnths are 19.8882 units and 2.11181 units