Question

Can some one help with 18 and 19

Answer 1

By by pythagorean theorem
12 (squared) + r (squared) = (8+r) squared
so 144 + r ( squared) = 64 + r (squared) +16r
so solving for r:
144 -64 = r squared –r squared + 16r
80 = 16r
so r = 80/16= 5

the second is the same
21 squared + r squared = (9 + r ) squared
441 + r squared = 81 + r squared + 18r
441 – 81 = r squared – r squared + 18r
r = 360/18 = 20