The altitude drawn to the hypotenuse of a right triangle separates the hypotenuse into two segments. The length of this altitude is the geometric mean between the lengths of these two segments.
x/h=h/y or h=sqrt(x*y)
Now, let's take a look at the given picture.
Using the theorem we recalled at the beginning, we can write an equation.
x=sqrt(8*12.5)
Now let's solve the equation.
Next we will take a square root of both sides of the equation. Notice that since y represents the side length, we will consider only the positive case when taking a square root of y^2.
In a right triangle, the sum of the squares of the lengths of the legs is equal to the square of the length of the hypotenuse.
a^2+ b^2= c^2
Next we will look at the given picture for the last time.
Having in mind that an altitude in a triangle divides this triangle into two right triangles, we can again use the Pythagorean Theorem to evaluate the value of z.
Next we will take a square root of both sides of the equation. Notice that since z represents the side length, we will consider only positive case when taking a square root of z^2.
