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We are given that the area of the square is 18 times the area of the triangle, and the dimensions of the triangle are provided as follows:

- Height of the triangle = \( \frac{5}{8} \) cm
- Base of the triangle = \( 6 \frac{2}{5} \) cm = \( 6.4 \) cm

### Step 1: Calculate the area of the triangle

The area of a triangle is given by the formula:

\[
\text{Area of triangle} = \frac{1}{2} \times \text{base} \times \text{height}
\]

Substituting the given values:

\[
\text{Area of triangle} = \frac{1}{2} \times 6.4 \, \text{cm} \times \frac{5}{8} \, \text{cm}
\]

### Step 2: Calculate the area of the square

The area of the square is 18 times the area of the triangle, so:

\[
\text{Area of square} = 18 \times \text{Area of triangle}
\]

### Step 3: Determine the side length of the square

The area of a square is given by:

\[
\text{Area of square} = (\text{side})^2
\]

Thus, to find the side length of the square, we solve:

\[
\text{side} = \sqrt{\text{Area of square}}
\]

### Step 4: Calculate the perimeter of the square

Finally, the perimeter of a square is given by:

\[
\text{Perimeter of square} = 4 \times \text{side}
\]

Let me compute these values now.The perimeter of the square is \( 24 \, \text{cm} \).

Would you like more details on any of the steps? Here are five related questions to further explore the topic:

1. How do you calculate the area of any polygon?
2. How would the solution change if the square's area was a different multiple of the triangle's area?
3. Can you find the length of the diagonal of the square?
4. How would the perimeter change if the triangle had a different base or height?
5. What other types of shapes can be related using their areas?

**Tip:** Remember that for triangles, the base and height must always be perpendicular to each other when calculating the area.

The area of the square is 18 times the area of the triangle. Work out the perimeter of the square. The triangle has a height of 5/8 cm and a base of 6 2/5 cm.

Learn how to calculate the perimeter of a square when given the area of a triangle. This problem uses area and perimeter formulas, making it suitable for students in Grades 8-10.

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