Question 1209058
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In the diagram, AB = BC and BD=DC=CE. AB=4 cm. Find the length of AE, in cm.
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From the diagram, BC = AB = 4 cm.


Also from the diagram, BD = DC = BC/2 = 4/2 = 2 cm.


Hence, AE = DC = 2 cm.


From point E, draw a line parallel to BC till the intersection with AB at the point G.


Then GE is a perpendicular to AB and BG = CE = 2 cm.


Hence, AG = 4 - 2 = 2 cm.


Thus triangle AGE is a right angled triangle with the legs GE = 4 and AG = 2 cm.


Then the hypotenuse AE = {{{sqrt(4^2 + 2^2)}}} = {{{sqrt(20)}}} = {{{2*sqrt(5)}}} cm = 4.472 cm  (approximately).


<U>ANSWER</U>.  AE = {{{2*sqrt(5)}}} = 4.472 cm  (approximately).
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Solved.