Question

Need help finding the missing length to the attached triangle.

Answer 1

1500

Explanation:

Use the right triangle altitude theorem.

x/900 = 2500/x

x^2 = 900 * 2500

x = sqrt(900 * 2500)

x = 30 * 50

x = 1500

Answer 2

1500

Explanation:

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

Now by geometric mean property:

`h = √(1600 * 900) \\ h = 40 * 30 \\ h = 1200 \: units \\ Next \: by \: Pythagoras \: Theorem: \\ {x}^(2) = {h}^(2) + {900}^(2) \\ {x}^(2) = {1200}^(2) + {900}^(2) \\ {x}^(2) = 1440000 + 810000 \\ {x}^(2) = 2,250,000 \\ x = √(2,250,000) \\ \huge \red{ \boxed{x = 1500\: units }}`