Question

se the relationship in 45-45-90 triangles to solve the following problem. If the hypotenuse of a triangle is 4 cm, what is the length of the leg?

Answer 1

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 use this formula to find the length of each leg.

Let \( x \) be the length of each leg. Then we have:

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

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

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

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

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

Therefore, the length of each leg of the triangle is \( 2\sqrt{2} \) cm.