Question

In the diagram, CE = 12 and BE = 5.

Based on the given information, AE =

Answer 1

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=√(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=√(119)\ units\\BE=5\ units`

substitute the values

`AE^(2)=√(119)^(2)+5^(2)`

`AE^(2)=144`

`AE=12\ units`

therefore

the answer is

The length of side AE is
`12\ units`

Answer 2

12 units

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=√(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.