Question

What is the value of y? NU=9, NM= 3, MT= 6, TN= y

Answer 1

6
`√(3)`

Explanation:

We have to use Pythagoras' identity twice to find y

The square on the hypotenuse is equal to the sum of the squares on the other two sides.

In right triangle MUT to find TU

TU² + 3² = 6², that is

TU² + 9 = 36 ( subtract 9 from both sides )

TU = 27 ( take the square root of both sides )

TU =
`√(27)` =
`√(9(3))` = 3
`√(3)`

In right triangle NUT to find y

y² = 9² + (3
`√(3)` )² = 81 + 27 = 108 ( take the square root of both sides )

y =
`√(108)` =
`√(36(3))` = 6
`√(3)`