Question

Find the value of x and simplify completely.

Answer 1

x=9√10

Given: A right triangle in which an altitude is drawn from the right angle vertex to the hypotenuse.

To find: 'x' the larger leg of triangle

Solution,

Using let rule for similarity in right triangle:

`(leg)/(part) = (hypotenuse)/(leg) \\ or \: (x)/(27) = (3 + 27)/(x) \\ or \: x * x = 27(3 + 27) \\ or \: x * x = 81 + 729 \\ or \: {x}^(2) = 810 \\ or \: {x}^(2) = 81 * 10 \\ or \: {x} = √(81 * 10) \\ or \: x = √(81) * √(10) \\ or \: x = \sqrt{ {(9)}^(2) } * √(10) \\ \: x = 9 √(10)`

Hope this helps...

Good luck on your assignment..