Question

ABC is right angle at c cd is perpendicular to if ac = 4 cm bc = 3cm then find cd

Answer 1

perpendicular to the hypotenuse will always divide the triangle into two triangles with the same properties as the original triangle.

Thus, the perpendicular AC divides right triangle ABD into two similar triangles ACB and DCA (which are also similar to big triangle ABD). Now, in these three triangles the ratio of the corresponding sides will be equal (corresponding sides are the sides opposite the same angles marked with red and blue on the diagram). 

So, CDAC=ACBCCDAC=ACBC --> CD4=43CD4=43 --> CD=163CD=163.