The hypotenuse of a 45 -45° -90° triangle measures 18 cm. what is the length of one leg of the triangle?

So the 45-45-90 triangle is considered to be a "special triangle" and has a rule with it. If the legs are x, then the hypotenuse is x√2. Since we know that the hypotenuse is 18, this means we can set up our equation as such:

From here we can solve for x. Firstly, divide both sides by √2.

Next, we want to simplify this expression and to do that we first have to rationalize the denominator. With the right side, multiply the numerator and denominator by √2:

Next, divide:

In short, the length of one leg of the triangle is 9√2 cm.

A 45-45-90 triangle is a special triangle: If the legs of the hypotenuse each equal x then the length of the hypotenuse is equal to x√2.

To find the length of one of the legs, all we need to do is find the value of "x".

The hypotenuse in a 45-45-90 triangle is equal to x√2.

In this case we are given the hypotenuse which equals 18cm.

x√2 = 18

to find the value of x divide both sides by √2

x√2 / √2 = 18 / √2

x = 18/√2 or 9√2 (the most simplified form)*

x is the length of one of the legs of a 45-45-90 triangle.

∠cbe and ∠deb are same-side interior angles.

i took the test

δabc ≅ δdcb by sas because

db ≅ ac . . given (side)

bc ≅ bc . . reflexive property (side)

∠dbc ≅ ∠ acb . . alternate interior angles where transversal bc crosses parallel lines bd and ac (included angle)