Find the lengths of the legs of a right triangle, if it is known that the sum of the lengths is 23 cm, and the area of the triangle is 60 cm².

Answer:   8 cm, 15 cmStep-by-step explanation:The area of a triangle is given by the formula ...   A = (1/2)bhwhere 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 + hThese 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.