Final answer:
The value of c that makes w² + 13w + c a perfect square trinomial is 169/4, and the binomial squared is (w + 13/2)².
Step-by-step explanation:
To find the value of c that makes w² + 13w + c a perfect square trinomial, we seek to write it as a binomial squared of the form (w + p)², where p is some number. Since the middle term is 13w, we need to find a p such that 2wp = 13w. Solving this, we get p = 13/2. To form a perfect square, c must be equal to p², so c = (13/2)² = 169/4. The trinomial can now be written as (w + 13/2)².