Question

What is the length of leg s of the triangle below?

Answer 1

Explanation:

Keep in mind that this triangle is a 45-45-90 triangle meaning that it's isosceles

This means that the other side is also equal to s

The best way to solve this is by using the pythagorean theorem

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

10
`√(2)` = c (because it's the hypotenuse or the longest side)

s = a

s= b

Substitute the values into the formula stated above

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

`s^(2)`+
`s^(2)` =(10
`√(2)`
`)^(2)`

Simplify

`2s^(2)` =
`(√(102) )^(2)`

`2s^(2)`= 102

Now continue simplifying till you completely solve it

`(2s^(2) )/(2)`=
`(102)/(2)`

`s^(2)`= 51

`\sqrt{s^(2) }` =
`√(51)`

s=
`√(51)`

I hope this helps!!!