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# Calculating similar lenghts

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I found ED and it was correct but I cant find out BE

Oct 4, 2018

#1
+8394
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∠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

Oct 4, 2018
#2
+101788
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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

Oct 4, 2018