Question

Find the unknown side length, x. Write your answer in the simplest radical form.

Answer 1

`x=√(41)\ units`

Explanation:

see the attached figure with letters to better understand the problem

we know that

In a right triangle the Pythagoras theorem formula is equal to

`c^(2) =a^(2) +b^(2)`

where

c is the hypotenuse

a,b are the legs of triangle

step 1

In the right triangle ABC find BC

`AB^(2) =AC^(2) +BC^(2)`

substitute the values

`52^(2) =48^(2) +BC^(2)`

`BC^(2)=52^(2)-48^(2)`

`BC^(2)=400`

`BC=20\ units`

step 2

In the right triangle CBF find CF

`BC^(2) =BF^(2) +CF^(2)`

substitute the values

`20^(2) =12^(2) +CF^(2)`

`CF^(2)=20^(2)-12^(2)`

`CF^(2)=256`

`CF=16\ units`

step 3

In the right triangle DEF find EF

`DF^(2) =ED^(2) +EF^(2)`

substitute the values

`13^(2) =5^(2) +EF^(2)`

`EF^(2)=13^(2)-5^(2)`

`EF^(2)=144`

`EF=12\ units`

step 6

Find the measure CE

`CE=CF-EF`

substitute

`CE=16-12=4\ units`

step 7

In the right triangle CDE find the value of x

`x^(2) =CE^(2) +ED^(2)`

substitute the values

`x^(2) =4^(2) +5^(2)`

`x^(2)=41`

`x=√(41)\ units`