The base AB & height BC of a right triangle ABC are A & B respectively?

Question

Find the length of the perpendicular from B to AC.

Answer 1

ab/ (a^2+b^2)^1/2

Answer 2

ABC is a right triangle with the right angle at B.

AC² = AB² + BC²

Let's call the point of intersection D of the perpendicular dropped from B to AC. We want to find BD. By similar triangles we have:

BD/BC = AB/AC
BD = (AB*BC) / √(AB² + BC²)

Answer 3

We know that the hypotenuse of this triangle is √(a²+b²). Let x be the length in question. The area of this triangle can be expressed in at least these two ways, having equal value:

(1/2)ab = (1/2)√(a²+b²) x

Therefore, x = (ab)/√(a²+b²)

Answer 4

sides of a 45-45-90 triangle are the same therefore the length of the perpendicular is c squared/2

Answer 5

draw a line from midpoint of line BC to the midpoint of line AC and assign x for the base of that triangle and y for its height.

so ..... x/y = A/B therefore x = y (A/B), this is the line perpendicular to line or height BC to line AC..
hope it helps