Question

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

Answer 1

Steps

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:

$x\sqrt{2} =18$

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

$x=\frac{18}{\sqrt{2}}$

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:

$\frac{18}{\sqrt{2}}*\frac{\sqrt{2}}{\sqrt{2}}=\frac{18\sqrt{2}}{2}\\\\\\x=\frac{18\sqrt{2}}{2}$

Next, divide:

$x=9\sqrt{2}$

Answer

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

Answer 2

Step-by-step explanation:

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.

*Note: 18 / √2 can be written as 18√2 / 2 which simplified becomes 9√2.

Answer: 9√2 cm