Question

In a 45° - 45° - 90° triangle , what is the measure of one of its legs if the hypotenuse is 32 cm?

Answer 1

16
`√(2)`

Explanation:

note that in a 45° - 45° - 90° triangle the legs are equal in length, since triangle is a right isosceles

let x be the length of the leg

using Pythagoras' identity on the triangle, then

x² + x² = 32²

2x² = 1024 ( divide both sides by 2 )

x² = 512 ( take the square root of both sides )

x =
`√(512)` = 16
`√(2)`

the legs have length 16
`√(2)`