Question

The hypotenuse of a 45-45-90 right triangle is 10?2. The legs are _____ Select one: a. ?2 b. 5 c. 20 d. 5?2 e. none of these

Answer 1

Option e is correct, as the length of legs are 10

none of these

Explanation:

In 45-45-90 special triangle:

The length of the hypotenuse is
`√(2)` times the length of a leg.

As per the statement:

The hypotenuse of a 45-45-90 right triangle is
`10√(2)` units.

then by definition:

`\text{Length of hypotenuse} =√(2) * \text{Length of a leg}`

Substitute the given values we have;

`10√(2)=√(2) * \text{Length of a leg}`

Divide both sides by
`√(2)` we get;

`10=\text{Length of a leg}`

Therefore, the length of legs are 10