Answer:
r=10
Step-by-step explanation:
We can use the Pythagorean theorm to solve
a^2 +b^2 = c^2
24^2 + r^2 =(16+r)^2
FOIL the last term
(16+r) (16+r) = 256+16r+16r+r^2
576 +r^2 = 256+16r+16r+r^2
Combine like terms
576 +r^2 = 256+32r+r^2
Subtract r^2 from each side
576 +r^2 -r^2 = 256+32r+r^2-r^2
576 = 256+32r
Subtract 256 from each side
576-256 = 256-256+32 r
320 = 32r
Divide by 32
320/32 = 32r/32
10 =r
