Question

Finding Hypotenuse Lengths. Find the length of the hypotenuse in

the 45°-45°-90° triangle. Write your answer in radical form.

Answer 1

6.
`2√(2)`

7.
`7√(2)`

8.
`√(10)`

9.
`8√(2)`

10.
`3`

11.
`2√(5)`

Explanation:

for all of these problems i used the pythagorean theorem, which is
`a^(2) + b^(2) = c^(2)`

6.

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

`8=c^(2)`

`√(8) =\sqrt{c^(2) }`

`2√(2)`

7.

`7^(2) + 7^(2) = c^(2)`

`49+49=c^(2)`

`98=c^(2)`

`√(98) =\sqrt{c^(2) }`

`7√(2)`

8.

`(√(5))^(2) +(√(5))^(2) =c^(2)`

`5+5=c^(2)`

`√(10)`

9.

`8^(2) +8^(2) =c^(2)`

`64+64=c^(2)`

`128=c^(2)`

`√(128) =\sqrt{c^(2) }`

`8√(2)`

10.

`(√(3)) ^(2) + (√(3)) ^(2) = c^(2)`

`3+3=c^(2)`

`9=c^(2)`

`√(9) =\sqrt{c^(2) }`

`3`

11.

`(√(10)) ^(2) + (√(10)) ^(2) = c^(2)`

`10+10=c^(2)`

`20=c^(2)`

`√(20) =\sqrt{c^(2) }`

`2√(5)`