Question

In this figure above, line l is parallel to m, segment BD is perpendicular to line m, and segment AC and segment BD intersect at E. What is the length of segment AC?

Answer 1

step 1

In the right triangle ADE

Apply Pythagorean Theorem

Find AE

AE^2=AD^2+DE^2

substitute the given values

AE^2=12^2+5^2

AE^2=169

AE=13 units

step 2

In this problem triangle ADE and triangle CBE are similar

that means ----> the ratio of its corresponding sides is proportional

so

AE/EC=DE/EB

substitute the given values

13/EC=5/1

EC=13/5

EC=2.6 units

step 3

Find AC

AC=AE+EC

AC=13+2.6=15.6 units

therefore'

AC=15.6 units