Question

Use the diagram of a right isosceles triangle to answer the question.

Information
An isosceles right triangle has a hypotenuse of 12 centimeters. The 2 legs are marked congruent to each other.

Question
What is the length of a leg of the triangle?

Answer options with 5 options
A.
StartRoot 6 EndRoot centimeters

B.
StartRoot 12 EndRoot centimeters

C.
StartRoot 36 EndRoot centimeters

D.
StartRoot 72 EndRoot centimeters

E.
StartRoot 142 EndRoot centimeters

Answer 1

In a right isosceles triangle, the lengths of the legs are equal, and the relationship between the lengths of the legs and the hypotenuse can be described using the Pythagorean theorem.

Let \( x \) be the length of each leg. For a right isosceles triangle, the relationship can be described as:

\[
x^2 + x^2 = (12)^2
\]

This simplifies to:

\[
2x^2 = 144
\]

Now, divide both sides by 2:

\[
x^2 = 72
\]

Taking the square root of both sides gives us:

\[
x = \sqrt{72}
\]

Now, we can simplify \(\sqrt{72}\):

\[
\sqrt{72} = \sqrt{36 \times 2} = 6\sqrt{2}
\]

However, since \(6\sqrt{2}\) is not in the answer options presented, we need to find the length of \(x\) in a different format based solely on the given options and the hypotenuse.

Since here in options, we have:

- A. \(\sqrt{6}\) centimeters
- B. \(\sqrt{12}\) centimeters
- C. \(\sqrt{36}\) centimeters
- D. \(\sqrt{72}\) centimeters
- E. \(\sqrt{142}\) centimeters

Our correct answer must match \(x = \sqrt{72}\) centimeters.

Thus, the answer is:

**D. \(\sqrt{72}\) centimeters**.