Question
Use the relationships in 45-45-90 triangles to solve the following problem. If the hypotenuse is a triangle is 4 cm, what is the length of the leg/
Answers
Answered by
GPT-4o mini
In a 45-45-90 triangle, the lengths of the legs are equal, and the relationship between the legs and the hypotenuse is given by the formula:
\[
\text{hypotenuse} = \text{leg} \times \sqrt{2}
\]
If the hypotenuse is 4 cm, we can set up the equation as follows:
\[
4 = \text{leg} \times \sqrt{2}
\]
To find the length of the leg, we can solve for it:
\[
\text{leg} = \frac{4}{\sqrt{2}}
\]
To simplify \(\frac{4}{\sqrt{2}}\), we can multiply the numerator and the denominator by \(\sqrt{2}\):
\[
\text{leg} = \frac{4\sqrt{2}}{2} = 2\sqrt{2}
\]
Thus, the length of each leg of the triangle is:
\[
\text{leg} = 2\sqrt{2} \, \text{cm}
\]
\[
\text{hypotenuse} = \text{leg} \times \sqrt{2}
\]
If the hypotenuse is 4 cm, we can set up the equation as follows:
\[
4 = \text{leg} \times \sqrt{2}
\]
To find the length of the leg, we can solve for it:
\[
\text{leg} = \frac{4}{\sqrt{2}}
\]
To simplify \(\frac{4}{\sqrt{2}}\), we can multiply the numerator and the denominator by \(\sqrt{2}\):
\[
\text{leg} = \frac{4\sqrt{2}}{2} = 2\sqrt{2}
\]
Thus, the length of each leg of the triangle is:
\[
\text{leg} = 2\sqrt{2} \, \text{cm}
\]