Use the relationships in 45-45-90 triangles to solve the following problem. If the hypotenuse of a triangle is 4 cm, what is the lenght of the leg?

Answer 1

In a 45-45-90 triangle, the legs are of equal length, and the relationship between the legs (let's call each leg \( x \)) and the hypotenuse \( h \) is given by the formula:

\[ h = x\sqrt{2} \]

Given that the hypotenuse \( h = 4 \) cm, we can set up the equation:

\[ 4 = x\sqrt{2} \]

To solve for \( x \), divide both sides by \( \sqrt{2} \):

\[ x = \frac{4}{\sqrt{2}} \]

Now, to simplify \( \frac{4}{\sqrt{2}} \), we can multiply the numerator and the denominator by \( \sqrt{2} \):

\[ x = \frac{4\sqrt{2}}{2} = 2\sqrt{2} \]

Thus, the length of each leg of the triangle is:

\[ \boxed{2\sqrt{2}} \text{ cm} \]

Answer 2

u sure

Answer 3

Yes, I am sure! Let's review the solution step-by-step to ensure accuracy:

For a 45-45-90 triangle, the relationship between the length of the legs \(x\) and the hypotenuse \(h\) is expressed as:

\[ h = x\sqrt{2} \]

Given that the hypotenuse \(h\) is 4 cm, we can substitute this value into the equation:

\[ 4 = x\sqrt{2} \]

To find the length of the leg \(x\), we can rearrange the equation:

\[ x = \frac{4}{\sqrt{2}} \]

Next, we simplify \( \frac{4}{\sqrt{2}} \). To do this, we multiply the numerator and the denominator by \( \sqrt{2} \) to rationalize the denominator:

\[ x = \frac{4 \sqrt{2}}{2} = 2\sqrt{2} \]

So, the length of each leg of the triangle is indeed:

\[ \boxed{2\sqrt{2}} \text{ cm} \]

Feel free to ask if you have any further questions!