Imagine you are a teacher. Explain to students how to construct a triangle whose perimeter is 124 mm, and the sides are in the ratio 2:3:4.

To construct a triangle with a perimeter of 124 mm and sides in the ratio 2:3:4, we first need to determine the lengths of each side.

Let the common ratio be x. Therefore, the sides of the triangle will be 2x, 3x, and 4x.

Since the perimeter of the triangle is 124 mm, we can set up an equation:

2x + 3x + 4x = 124
9x = 124
x = 124/9
x = 13.78

Now, we can find the lengths of each side:
Side 1: 2x = 2(13.78) = 27.56 mm
Side 2: 3x = 3(13.78) = 41.34 mm
Side 3: 4x = 4(13.78) = 55.12 mm

Now that we have the lengths of each side, we can construct the triangle by drawing a line segment of 27.56 mm, another line segment of 41.34 mm, and a third line segment of 55.12 mm. Connect the endpoints of the line segments to form a triangle.

Make sure to use a ruler and protractor to ensure accurate measurements and angles.

Step 1: Find the Total Number of Parts

The ratio of the sides is 2:3:4, which can be expressed as 2x:3x:4x, where x represents an unknown number. To find the total number of parts, add the coefficients of x:

```
2x + 3x + 4x = 9x
```

Step 2: Convert the Perimeter to Number of Parts

The perimeter is 124 mm, so convert it to the number of parts by dividing by x:

```
Perimeter / x = Number of parts
124 mm / x = 9x
```

Step 3: Solve for x

Solve the above equation for x:

```
x = 124 mm / 9x = 13.78 mm
```

Step 4: Find the Length of Each Side

Substitute the value of x into the expressions for the side lengths:

- First side: 2x = 2 - 13.78 mm = 27.56 mm
- Second side: 3x = 3 - 13.78 mm = 41.34 mm
- Third side: 4x = 4 - 13.78 mm = 55.12 mm

Step 5: Construct the Triangle

Using a ruler and protractor, draw three line segments with the following lengths:

- 27.56 mm
- 41.34 mm
- 55.12 mm

Step 6: Connect the Segments

Join the ends of the line segments to form a triangle. The perimeter of the triangle will be 124 mm, and the sides will be in the ratio 2:3:4.

Answer neded