Answer:
8 cm, 15 cm
Explanation:
The area of a triangle is given by the formula ...
A = (1/2)bh
where b is the base length and h is the height perpendicular to the base.
In a right triangle, it is convenient to use the leg lengths for b and h. Thus, we have two relations describing these values:
60 = (1/2)bh
23 = b + h
These equations give rise to a quadratic, which can be solved by various means. I prefer to go directly to a graphing calculator and let it show me the solution(s).
The leg lengths are 8 cm and 15 cm.
_____
The quadratic in B is ...
120 = b(23 -b) . . . . substitute for h, clear fractions
b^2 -23b +120 = 0 . . . put in standard form
(b -8)(b -15) = 0 . . . . . . factored. b = 8 or 15; h = 15 or 8.