A 63 cm long wire is to be cut into two pieces such that one piece will be `2/5` as long as the other. How many centimetres will the shorter piece be?

Options

A. 9
B. 18
C. 36
D. 45

Answer

To solve the problem, we need to determine the lengths of the two pieces of wire when one piece is \( \frac{2}{5} \) the length of the other. Let's denote the length of the longer piece as \( x \) cm. Then, the length of the shorter piece can be expressed as \( \frac{2}{5}x \) cm.

### Step-by-step Solution:

1. **Define the Variables**:
Let the length of the longer piece be \( x \) cm. Therefore, the length of the shorter piece will be \( \frac{2}{5}x \) cm.

2. **Set Up the Equation**:
Since the total length of the wire is 63 cm, we can set up the equation:
\[ x + \frac{2}{5}x = 63 \]

3. **Combine Like Terms**:
To combine the terms on the left side, we can convert \( x \) into a fraction:
\[ x = \frac{5}{5}x \]
Now, the equation becomes:
\[ \frac{5}{5}x + \frac{2}{5}x = 63 \]
\[ \frac{7}{5}x = 63 \]

4. **Solve for \( x \)**:
To isolate \( x \), multiply both sides of the equation by \( \frac{5}{7} \):
\[ x = 63 \times \frac{5}{7} \]
\[ x = 9 \times 5 = 45 \text{ cm} \]

5. **Find the Length of the Shorter Piece**:
Now that we have \( x \), we can find the length of the shorter piece:
\[ \text{Shorter piece} = \frac{2}{5}x = \frac{2}{5} \times 45 = 18 \text{ cm} \]

### Final Answer:
The length of the shorter piece is **18 cm**.