If a 70-cm cord is cut into two parts with a ratio of 3:4, what is the length of the longer part?

To determine the length of the longer part when a 70-cm cord is cut into two parts with a ratio of 3:4, it’s essential to understand how ratios work in this context.

In a ratio of 3:4, the two parts can be represented as 3x and 4x, where x is a common factor. To find the total parts represented by the ratio, you add the parts together:

3 + 4 = 7 parts in total.

Next, since the total length of the cord is 70 cm, you can set up the equation:

3x + 4x = 70.

This simplifies to:

7x = 70.

To find the value of x, divide both sides by 7:

x = 10.

Now, you can determine the lengths of the two parts. The shorter part, represented by 3x, would be:

3 * 10 = 30 cm.

The longer part, represented by 4x, would thus be:

4 * 10 = 40 cm.

Hence, the length of the longer part is indeed 40 cm. This confirms that the option indicating 40 cm is the correct length for the longer segment when