Answer:
N=15 O=17
Explanation:
since we know this is a rectangle and the lines are diagonals we can assume they create right triangles. For line N we set up the Pythagorean Theorem which is a^2 + b^2 = c^2 and to find N we plug in 9 for a and 12 for b. 9^2 + 12^2 = c^2 c^2 = 225 so now we find the square root of c^2 so c or in this case N = 15, now we repeat this same exact sequence for O but N is now our base and 8 is our height of the triangle so we will plug in 8 for a and 15 for b: 8^2 + 15^2 = c^2 c^2 = 289 and the square root of 289 is 17.