Question

What is the value of y?

3 StartRoot 3 EndRoot units
6 StartRoot 3 EndRoot units
9 StartRoot 3 EndRoot units
12 StartRoot 3 EndRoot units

Answer 1

B

Explanation:

I know its right

Answer 2

Note: You forgot to add the diagram, so I found the missing diagram and attached below, based on which I am solving your query. Hopefully, it would clear your concepts anyways.

Answer:

Option B is correct, as
`\boxed{y=6√(3)}`

Explanation:

From the attached figure,

Δ
`MTU` is a right triangle.

Applying Pythagoras theorem,

`TM^2=TU^2+MU^2`

`\left(6\right)^2=TU^2+\left(3\right)^2`

`\left(6\right)^2-\left(3\right)^2\:=TU^2`

switching sides

`TU^2=\left(6\right)^2-\left(3\right)^2\:`

`TU^2=36-9`

`TU^2=27`

Note that Δ
`NTU` s also right triangle.

`\:NT^2\:=\:TU^2\:+\:NU^2`

`=27\:+\:9^2` ∵
`TU^2=27`

`=108`

`\mathrm{For\:}x^2=f\left(a\right)\mathrm{\:the\:solutions\:are\:}x=√(f\left(a\right)),\:\:-√(f\left(a\right))`

`NT=√(108),\:NT=-√(108)`

But length of a side can not be negative, so ignore the negative solution.

so

`NT=√(108)`

`y=6√(3)` ∵
`NT = y`

Therefore, option B is correct, as
`\boxed{y=6√(3)}`