Question

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

Answer 1

Answer:

6$\sqrt{3}$

Step-by-step 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 = $\sqrt{27}$ = $\sqrt{9(3)}$ = 3$\sqrt{3}$

In right triangle NUT to find y

y² = 9² + (3$\sqrt{3}$ )² = 81 + 27 = 108 ( take the square root of both sides )

y = $\sqrt{108}$ = $\sqrt{36(3)}$ = 6$\sqrt{3}$