Question
Special Right Triangles Quick Check 4 of 54 of 5 Items Question 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 length of the leg?(1 point) Responses 23–√ cm 2 Start Root 3 End Root cm 22–√ cm 2 Start Root 2 End Root cm 42–√ cm 4 Start Root 2 End Root cm 2 cm 2 cm Skip to navigation page 15 of 15
Answers
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:
\[
\text{Hypotenuse} = \text{Leg} \times \sqrt{2}
\]
In this case, the hypotenuse is 4 cm. We can let the length of each leg be \( x \):
\[
4 = x \times \sqrt{2}
\]
To solve for \( x \), divide both sides by \( \sqrt{2} \):
\[
x = \frac{4}{\sqrt{2}}
\]
To rationalize the denominator, multiply the numerator and denominator by \( \sqrt{2} \):
\[
x = \frac{4\sqrt{2}}{2} = 2\sqrt{2}
\]
So, the length of each leg is \( 2\sqrt{2} \) cm.
Among the options provided, the correct response is:
**\( 2\sqrt{2} \) cm**.
\[
\text{Hypotenuse} = \text{Leg} \times \sqrt{2}
\]
In this case, the hypotenuse is 4 cm. We can let the length of each leg be \( x \):
\[
4 = x \times \sqrt{2}
\]
To solve for \( x \), divide both sides by \( \sqrt{2} \):
\[
x = \frac{4}{\sqrt{2}}
\]
To rationalize the denominator, multiply the numerator and denominator by \( \sqrt{2} \):
\[
x = \frac{4\sqrt{2}}{2} = 2\sqrt{2}
\]
So, the length of each leg is \( 2\sqrt{2} \) cm.
Among the options provided, the correct response is:
**\( 2\sqrt{2} \) cm**.