Answer:
2sqrt(5)
Step-by-step explanation:
The left triangle is a right triangle so we can use the Pythagorean theorem
a^2+b^2 = c^2 where a and b are the legs and c is the hypotenuse
5^2 + b^2 = 9^2
b^2 = 9^2 - 5^2
b^2 = 81-25
b^2 =56
Taking the square root of each side
b = sqrt(56) = sqrt(4*14) = 2 sqrt(14)
The right side is also a right triangle so we can use the Pythagorean theorem
a^2+b^2 = c^2 where a and b are the legs and c is the hypotenuse
x^2 + 6^2 = (sqrt(56))^2
x^2 +36 = 56
x^2 = 56-36
x^2 = 20
Taking the square root
sqrt(x^2) = sqrt(20) = sqrt(4*5) = 2sqrt(5)
