Question

In the diagram, CE = 12 and BE = 5. Based on the given information, AE =

Answer 1

Answer:

12 units

Step-by-step explanation:

From the given figure, it can be seen that AB=BC, thus

From ΔBEC, using the Pythagoras theorem, we have

$(EC)^{2}=(BE)^{2}+(BC)^{2}$

$(12)^2=(5)^2+(BC)^2$

$144=25+(BC)^2$

$119=(BC)^2$

$BC=\sqrt{119} units$

Now, from ΔABE, using the Pythagoras theorem, we have

$(AE)^2=(BE)^2+(AB)^2$

$(AE)^2=25+119$

$(AE)^2=144$

$AE=12 units$

Thus, the measure of AE is 12 units.

Answer 2

we know that

AB=BC ------> given problem

Step $1$

In the right triangle BCE

Find the value of BC

Applying the Pythagorean Theorem

$CE^{2}=BC^{2}+BE^{2}\\BC^{2}=CE^{2}-BE^{2}$

in this problem we have

$CE=12\ units\\BE=5\ units$

substitute the values

$BC^{2}=12^{2}-5^{2}\\BC^{2}= 119\\BC=\sqrt{119}\ units$

Step $2$

In the right triangle ABE

Find the value of AE

Applying the Pythagorean Theorem

$AE^{2}=AB^{2}+BE^{2}$

in this problem we have

$AB=\sqrt{119}\ units\\BE=5\ units$

substitute the values

$AE^{2}=\sqrt{119}^{2}+5^{2}$

$AE^{2}=144$

$AE=12\ units$

therefore

the answer is

The length of side AE is $12\ units$