What is the value of x in the figure below in this diagram abd~cad

given abd~cad (note order of the letters are important in determining corresponding sides.

from similar triangles, we know that corresponding sides are proportional.

this means that

abd/cad = abd/cad

using x=ad, and substituting values for side lengths

x/13=3/x

cross multiply

x*x=3*13 => x^2=39 => x=sqrt(39)

alternatively, use the metric relation

for any right triangle with an altitude from the right angle.

ad^2=cd*db

=> x^2=13*3=39, or x=sqrt(39).

the other metric relations are:

ac^2=cd*cb

ab^2=bd*dc

and finally

ab*ac=ad*cb

square root of 39

step-by-step explanation:

set up : x/3=39/x

cross multiply

x^2=39

find the square root of 39

6.244 or square root of 39

22

step-by-step explanation: