MATH HELP! how do you answers this question

The hypotenuse of a right triangle has length 17 cm.
The sum of the legs is 23 cm.
What are their lengths?
x^2 + y^2 = 17^2
(x + y)^2 = 23^2
2xy = 40 x 6
xy = 120
x + y = 23
8 cm
15 cm

try 6 since the Hyp is 17 and the Legs is 23 basiclly its saying what is the legs and 17 + 6 = 23 id try that i remember doing this a few months back but not quite sure

let the legs be x and 23-x, we have x^2 + (23-x)^2 = 17^2

so 2x^2 - 46x + (529 - 289) = 0

x^2 - 23x + 120 = 0

this is a standard quadratic equation, x = 15 or 8

c^2 = a^2 + b^2

a + b = 23

17^2 = a^2 + b^2

a^2 + b^2 = 289

a + b = 23

a = 23 - b

(23 - b)^2 + b^2 = 289

529 - 46*b + b^2 + b^2- 289 = 0

2*b^2 - 46*b + 240 = 0

b^2 - 23*b + 120 = 0

(b - 8)*(b - 15) = 0

b1 = 8
b2 = 15

a = 23 - b

a1 = 15
a2 = 8

c^2 = a^2 + b^2

c^2 = 225 + 64 = 289

c^2 = 64 + 225 = 289

Answer:

a1 = 15, b1 = 8

a2 = 8, b2 = 15

thier lengths are 15 and 20