ABC is an isosceles triangle right angled at A. forces of magnitude `2sqrt(2),5 and 6` act along BC, CA and AB respectively. The magnitude of their resultant force is

Options

A. 4
B. 5
C. `11+2sqrt(2)`
D. 30

Explanation

To solve the problem, we need to find the resultant of three forces acting on an isosceles right triangle ABC, where A is the right angle. The forces are acting along the sides of the triangle as follows:

1. Force of magnitude \(2\sqrt{2}\) along BC
2. Force of magnitude \(5\) along CA
3. Force of magnitude \(6\) along AB

### Step-by-Step Solution:

**Step 1: Understand the Triangle Configuration**
- Since triangle ABC is isosceles and right-angled at A, we have \(AB = AC\).
- The angles at B and C are both \(45^\circ\).

**Hint:** Visualize the triangle and label the sides appropriately.

**Step 2: Draw the Forces**
- Draw the triangle ABC with the right angle at A.
- Indicate the forces acting along the sides:
- Force \(F_{BC} = 2\sqrt{2}\) along BC.
- Force \(F_{CA} = 5\) along CA.
- Force \(F_{AB} = 6\) along AB.

**Hint:** Use arrows to represent the direction and magnitude of each force.

**Step 3: Resolve the Forces into Components**
- The force \(F_{BC}\) makes an angle of \(45^\circ\) with both axes.
- Resolve \(F_{BC}\) into its components:
- \(F_{BCx} = 2\sqrt{2} \cos(45^\circ) = 2\)
- \(F_{BCy} = 2\sqrt{2} \sin(45^\circ) = 2\)

**Hint:** Remember that \(\cos(45^\circ) = \sin(45^\circ) = \frac{1}{\sqrt{2}}\).

**Step 4: Combine the Forces in the Vertical Direction**
- The vertical forces are:
- Upward force \(F_{AB} = 6\)
- Downward component of \(F_{BC} = 2\)
- The resultant vertical force \(F_{R_y} = 6 - 2 = 4\).

**Hint:** Keep track of the direction of each force when adding them.

**Step 5: Combine the Forces in the Horizontal Direction**
- The horizontal forces are:
- Leftward force \(F_{CA} = 5\)
- Rightward component of \(F_{BC} = 2\)
- The resultant horizontal force \(F_{R_x} = 5 - 2 = 3\).

**Hint:** Again, pay attention to the direction of the forces.

**Step 6: Calculate the Magnitude of the Resultant Force**
- Use the Pythagorean theorem to find the magnitude of the resultant force:
\[ R = \sqrt{F_{R_x}^2 + F_{R_y}^2} = \sqrt{3^2 + 4^2} = \sqrt{9 + 16} = \sqrt{25} = 5. \]

**Hint:** The resultant force is the hypotenuse of the right triangle formed by the horizontal and vertical components.

### Final Result:
The magnitude of the resultant force is \(5\) Newtons.