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.

  8 cm, 15 cm

Step-by-step 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.

b

step-by-step explanation:

calculate the scale factor as the ratio of corresponding sides, image to original, that is

scale factor = = = = 1