What is the value of y?3(Square Root)3 units6(Square Root)3 units9(Square Root)3units12(Square Root)3 units

Answer:- The value of y=6√3 units.
Explanation:-Given: Δ TNM is a right triangle, where TN=y , NU=9 units ,UM=3 units, TM=6 units.Now, we can see that NM=NU+UM⇒NM=9 units + 3 units=12 unitsAs Δ TNM is a right triangle , then by Pythagoras theorem[tex](Hypotenuse)^2=(Perpendicular)^2+(Base)^2\\\Rightarrow12^2=y^2+6^2\\\Rightarrow\ y^2=12^2-6^2\\\Rightarrow\ y^2=144-36=108\\\Rightarrow\ y=\sqrt{108}=6 \sqrt{3}[/tex]Thus y=6√3units.Pythagoras theorem states that in a right triangle the square of the longest side is equal to the sum of the squares of the other two sides.