Answer:
Step-by-step explanation:
use the pythagorean theorem
a^2 +b^2 = c^2 where c is the hypotenuse and a and b are the legs
1. x^2 + (sqrt(7))^2 =(sqrt(19)^2
x^2 +7 = 19
subtract 7 from both sides
x^2 = 12
take the square root
x = sqrt(12)
x = sqrt(4) sqrt(3)
x = 2sqrt(3)
2. x^2 + 12^2 = 13^2
x^2 +144=169
subtract 144 from each side
x^2 = 25
take the square root of each side
sqrt(x^2) = sqrt(25)
x = 5
3. 5^2 + 6^2 = x^2
25 + 36 = x^2
61 = x^2
take the square root of each side
x = sqrt(61)
4. 10^2 + 24^2 = x^2
100 +576 = x^2
676 = x^2
sqrt(676) = sqrt(x^2)
26 =x
5. x^2 + x^2 = (8sqrt(2))^2
2x^2 = 8^2 *(sqrt(2))^2
2x^2 = 64*2
divide by 2
x^2 = 64
take the square root on each side
sqrt(x^2) =sqrt(64)
x = 8
6. 6^2 + x^2 = 15^2
36+x^2 = 225
x^2 = 189
sqrt(x^2) = sqrt(189)
x = sqrt(9*21)
x = 3sqrt(21)
