Question

Find the value of Y
.....

Answer 1

`y = 6 √(3) \: units`

Explanation:

In order to find the value of y, first we need to find the length of the perpendicular dropped from one of the vertices of the triangle to its opposite side.

By geometric mean theorem:

Length of the perpendicular

`=√(9* 3)`

`=√(27)\: units`

Next, by Pythagoras theorem:

`{y}^(2) = {9}^(2) + {( √(27) )}^(2) \\ \\ {y}^(2) = 81 + 27 \\ \\ {y}^(2) = 108 \\ \\ y = √(108) \\ \\ y = √(36 * 3) \\ \\ y = \sqrt{ {6}^(2) * 3} \\ \\ y = 6 √(3) \: units`