What is AE ? Enter your answer in the box. _____units

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1 Answer
Jan 18, 2018

#AE=20# units

Explanation:

We are told that #AB# and #CD# are parallel, and therefore #/_AEB# and #/_CED# are the same. This tells us that the two triangles are similar shapes.

In terms of similarity #AE=ED#, but not the values, just the parts of the triangle they belong to.

The left hand triangle is #10/4# times bigger than the right hand triangle. So, #10/4(x+3)=2x+10#

#(10x)/4+30/4=2x+10#

#30/4-10=2x-(10x)/4#

#30/4-(10*4)/(1*4)=(2x*4)/(1*4)-(10x)/4#

#30/4-40/4=(8x)/4-(10x)/4#

#-10/4=-(2x)/4#

#-10=-2x#

#x=5#

#AE=2x+10#

#AE=2(5)+10=10+10=20#