The length of BC is equal to ab divided by 20.
In the given diagram, segment BC is perpendicular to segment CA and segment CD is perpendicular to segment BA. We can use the corollary of the Right Triangle Altitude Theorem to find the length of BC.
The corollary states that if a line is perpendicular to a side of a right triangle, then it is also perpendicular to the hypotenuse.
Therefore, CD is perpendicular to BA, which means that CD is the altitude of triangle ABC.
Using the formula for the area of a right triangle (area = 1/2 * base * height), we have:
1/2 * BC * AC = 1/2 * CD * BA
Since CD = f and BA = d + AD, we can substitute the given values:
1/2 * BC * AC = 1/2 * f * (d + e)
Simplifying the equation, we get:
BC * AC = f * (d + e)
Substituting the given values, we have:
a * b = f * (4 + 16)
Simplifying further, we get:
ab = 20f
Therefore, f = ab/20.
The probable question may be:
In the diagram shown, segment BC is perpendicular to segment CA and segment CD is perpendicular to segment BA. Use the corollary of the Right Triangle Altitude Theorem to find f.
BC=a, BD=d=4, AD=e=16, AC=b, CD=f