Each leg of a 45-45-90 triangle has a length of 6 units. What is the length of its hypotenuse?A.6 unitsB.12 unitsC.3 unitsD.6 unitsSUBMITarrow_backPREVIOUS

1. Break Down the Problem

We need to calculate the length of the hypotenuse of a 45-45-90 triangle given that each leg is 6 units long. A 45-45-90 triangle is an isosceles right triangle, where the legs are of equal length.

2. Relevant Concepts

The relationship between the legs and the hypotenuse in a 45-45-90 triangle can be described with the following formula: $\text{Hypotenuse} = \text{Leg} \times \sqrt{2}$

3. Analysis and Detail

Given that each leg $a$ is 6 units: $\text{Hypotenuse} = a \times \sqrt{2} = 6 \times \sqrt{2}$ Calculating $6 \times \sqrt{2}$, we know that $\sqrt{2} \approx 1.414$: $6 \times \sqrt{2} \approx 6 \times 1.414 \approx 8.484$

4. Verify and Summarize

Thus, the exact length of the hypotenuse is $6\sqrt{2}$. To summarize, we have calculated that the hypotenuse of this 45-45-90 triangle, given each leg is 6 units, is approximately 8.484 units.

Final Answer

The length of the hypotenuse is $6\sqrt{2}$ units, approximately 8.484 units. However, none of the provided options (A, B, C, D) match the actual hypotenuse length.