Question

Finding Leg Lengths. Find the length of a leg in the 45°-45°-90°
triangle.

Answer 1

12.
`x=10`

13.
`x=4`

14.
`x=5`

15.
`x=1`

16.
`x=8`

17.
`x=14`

Explanation:

for these i also used the pythagorean theorem (
`a^(2)+b^(2)=c^(2)`)

`a` and
`b` are the legs,
`c` is the hypotenuse

12.

`x^(2) +x^(2) =(10√(2) )^(2)`

`2x^(2) =200`

`x^(2) =100`

`x=10`

13.

`x^(2) +x^(2) =(4√(2) )^(2)`

`2x^(2) =32`

`x^(2) =16`

`x=4`

14.

`x^(2) +x^(2) =(5√(2) )^(2)`

`2x^(2) =50`

`x^(2) =25`

`x=5`

15.

`x^(2) +x^(2) =(√(2) )^(2)`

`2x^(2) =2`

`x^(2) =1`

`x=1`

16.

`x^(2) +x^(2) =(8√(2) )^(2)`

`2x^(2) =128`

`x^(2) =64`

`x=8`

17.

`x^(2) +x^(2) =(14√(2) )^(2)`

`2x^(2) =392`

`x^(2) =196`

`x=14`