Math Question Help! ( triangles)

The hypotenuse of a right triangle has length 17cm. The sum of the lengths of the legs is 23cm. What are their lengths?

x=length of base
y=other leg

x+y=23 or x=23-y

x^2+y^2= 17^2

(23-y)^2 +y^2 =17^2
529-46y+y^2+y^2=289

2y^2-46y+240=0
y^2-23y+120=0
(y-15)(y-8)=0
y=15 and y= 8

so you can have sides of (8,15) check it 8+15=23 sqrt(8^2+15^2)==> sqrt (64+225)==>17

17^2 = a^2 + (23-a)^2
17^2 = a^2 + 23^2 + a^2 - 46a
a^2 - 23a + 120 = 0
(a-15)(a-8) = 0
Sides are 15cm and 8cm

15 & 8