+9466 ∠ABE ≅ ∠ACD because they are corresponding angles.
∠AEB ≅ ∠ADC because they are corresponding angles.
So by AA similarity, △ABE ~ △ACD .
Let's let the scale factor from △ACD to △ABE be s .
Each side of △ABE is equal to s times the corresponding side of △ACD.
In other words....to get from △ACD to △ABE, multiply each side of △ACD by s .
So we know that....
AB = AC * s
And... AB = 20 cm ...and... AC = 20 cm + 5 cm = 25 cm
20 = 25 * s
Divide both sides of the equation by 25 .
20/25 = s
0.8 = s
The scale factor is 0.8 , so each side of △ABE is 0.8 times the corresponding side of △ACD.
That means....
BE = 0.8 * CD
BE = 0.8 * 18 cm
BE = 14.4 cm
+128474 Thanks, hectictar !!
Another approach is to note that a segment drawn parallel to the base of a triangle, divides the sides in equal proportions
Therefore for (a)
BC /AB = ED /AE
5 /20 = ED / 26
1/4 = ED / 26 multiply both sides by 26
26 (1/4) = ED = 26/4 = 13/2 = 6.5
(b) Also...we have that...since triangle ABE is similar to triangle ACD...then
BE / AB = CD /AC
BE / 20 = 18/ 25 multiply both sides by 20
BE = (18/25) * 20 = 14.4
