Question

How do I solve for X with the base numbers on a right triangle. (Please give an explanation and an answer, I need to know how it works.)

Answer 1

Let's label the 3 points as A;B;C, where BC is the hypotenuse and AB is the shortest side, and x as AH.

We can see that triangle AHC is similar to triangle CAB, and triangle ACH is similar to triangle BCA, so therefore triangle AHC is similar to triangle CHA (i might've messed up the order but you get it)

Because they are similar, we get the ratio : x/12 = 40/x, or x^2 = 480.

So, x =
`√(480)`, or 21.9 (1 d.p)

Answer 2

• 21.9 units

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According to the right triangle altitude theorem:

• the altitude on the hypotenuse is equal to the geometric mean of line segments formed by altitude on the hypotenuse.

We see x is the altitude and 12 & 40 are the segments formed on the hypotenuse.

Applied to the given triangle, we get following equation:

• 
  `x=√(12*40) =√(480) =21.9\ units`