Option A:
The simplest radical form of x is [tex]3\sqrt{15}[/tex].
Solution:
Hypotenuse = 16 in
Two sides are 11 in and x.
To find the value of x:
Pythagoras theorem:
In a right angle triangle, the hypotenuse is equal to the sum of the other two sides.
[tex]11^2+x^2=16^2[/tex]
[tex]121+x^2=256[/tex]
Subtract 121 from both sides of the equation.
[tex]121+x^2-121=256-121[/tex]
[tex]x^2=135[/tex]
Taking square root on both sides of the equation.
[tex]\sqrt {x^2}=\sqrt {135}[/tex]
[tex]x=3\sqrt {15}[/tex]
Hence option A is the correct answer.
Hence the simplest radical form of x is [tex]3\sqrt{15}[/tex].
