Answer :

Number 1 is A; using the Pythagorean formula, you get 12 squared + 4 squared is equal to the length of AG squared 

Number 2 is about 14 inches; using the Pythagorean formula you get length of DG, and using the Pythagorean formula again, u can find the length of CG
RedRicin
Question 1: Use the Pythagorean theorem.

Since DC and CG are 5 and 12, DG is 13. (This is an easy-to-recognize Pythagorean Triple btw)

Since AD and DG are 4 and 13, AG² is 4² + 13² = 16 + 169 = 185. √185 ≈ 13.6.

Question 2: This time we're working in reverse. If AG is 15 and AD is 9, then DG is 12. (This is another Pythagorean Triple, a multiple of 3, 4, 5)

If DG is 12 and DC is 10, CG² + 10² = 12² ⇒ CG² + 100 = 144. CG² = 44. √44 ≈ 6.6.