Question

Altitude on the hypotenuse of a right angled triangle divides it in two parts of length 4cm and 9cm. Find the length of altitude.

Answer 1

Answer:

6

Step-by-step explanation:

Call the triangle ABC, with the right angle at C, and let D be the foot of the altitude from C.  We are given that AD = 4 and BD = 9 (or the other way around, but just swap the labels on A and B in that case).  We need to find CD.

Now triangle ACD is similar to triangle ABC (AA rule, since both have right angles and they share the angle at A).

Similarly, triangles CBD and ABC are similar.

It follows that triangle ACD is similar to triangle CBD.

Therefore

AD / CD = CD / BD

which rearranges to be

CD² = AD . BD = 4 x 9 = 36

and finally

CD = 6.