SOLUTION: In the diagram, AB = BC and BD=DC=CE. AB=4 cm. Find the length of AE, in cm. https://ibb.co/8KwNR4r

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Question 1209058: In the diagram, AB = BC and BD=DC=CE. AB=4 cm. Find the length of AE, in cm.
https://ibb.co/8KwNR4r
Found 2 solutions by ikleyn, math_tutor2020:
Answer by ikleyn(52817)   (Show Source): You can put this solution on YOUR website!
.
In the diagram, AB = BC and BD=DC=CE. AB=4 cm. Find the length of AE, in cm.
https://ibb.co/8KwNR4r
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

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 =  =  =  cm = 4.472 cm  (approximately).


ANSWER.  AE =  = 4.472 cm  (approximately).

Solved.



Answer by math_tutor2020(3817)   (Show Source): You can put this solution on YOUR website!

Answer:
Exact length = cm
Approximate length = 4.47214 cm
This approximate value will slightly vary depending how you round it.


Explanation

Let's place point B at the origin.
4 units above B is point A(0,4)

AB = BC = 4
Since BC = 4, we move 4 units to the right of B to arrive at C(4,0)

BD = DC tells us that D is the midpoint of BC, so BD = DC = CE = 2

From point C move 2 units up to arrive at E(4,2)

We can use the distance formula to find out how far it is from A(0,4) to E(4,2)


Plug in (x1,y1) = (0,4) and (x2,y2) = (4,2)















Segment AE is exactly cm long. This approximates to 4.47214 cm.

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A slight alternate route:

From point E, draw a horizontal line until reaching the y axis. This forms right triangle EGA where G is on the same level as E and directly below point A.


Let's get rid of any points or lines we don't need.


We have a right triangle with horizontal leg of GE = 4 and vertical leg GA = 2
Use the Pythagorean theorem to determine solves to which is the hypotenuse of this right triangle. And it's also the distance from A to E.

As you can probably tell (or know by now), the distance formula is a modified version of the Pythagorean theorem.
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