Question

Need help finding the missing length to the attached triangle.

Answer 1

65 units

Explanation:

Let the length of the perpendicular dropped from the right angle to the hypotenuse be h units.

Now by geometric mean property:

`h = √(144 * 25) \\ h = 12 * 5 \\ h = 60 \: units \\ Next \: by \: Pythagoras \: Theorem: \\ {x}^(2) = {h}^(2) + {25}^(2) \\ {x}^(2) = {60}^(2) + {25}^(2) \\ {x}^(2) = 3600 + 625 \\ {x}^(2) = 4225 \\ x = √(4225) \\ \huge \red{ \boxed{x = 65\: units }}`