In an isosceles right angled triangle, what is the length of the equal sides of the triangle, if its hypotenuse is `6sqrt(2)` cm?

Options

A. `3sqrt(2) cm`
B. 6 cm
C. 12 cm
D. 5 cm

Answer

To find the length of the equal sides of an isosceles right-angled triangle when the hypotenuse is given as \(6\sqrt{2}\) cm, we can follow these steps:

### Step 1: Understand the properties of the triangle
In an isosceles right-angled triangle, the two sides that form the right angle are equal in length. Let's denote the length of each of these equal sides as \(x\).

### Step 2: Apply the Pythagorean theorem
According to the Pythagorean theorem, the relationship between the sides of a right triangle is given by:
\[ a^2 + b^2 = c^2 \]
where \(c\) is the hypotenuse. In our case:
\[ x^2 + x^2 = (6\sqrt{2})^2 \]

### Step 3: Simplify the equation
Combine the left side:
\[ 2x^2 = (6\sqrt{2})^2 \]

### Step 4: Calculate the square of the hypotenuse
Now calculate the square of the hypotenuse:
\[ (6\sqrt{2})^2 = 6^2 \cdot (\sqrt{2})^2 = 36 \cdot 2 = 72 \]
So, we have:
\[ 2x^2 = 72 \]

### Step 5: Solve for \(x^2\)
Now, divide both sides by 2:
\[ x^2 = \frac{72}{2} = 36 \]

### Step 6: Find \(x\)
To find \(x\), take the square root of both sides:
\[ x = \sqrt{36} = 6 \]

### Conclusion
Thus, the length of the equal sides of the isosceles right-angled triangle is \(6\) cm.