Alex paid some one $ 8112 to mow his Square yard at the rate of $12 per square meter?. what is the length of one side of the yard?

To find the length of one side of Alex's square yard, we need to solve this problem step by step.

### Step 1: Calculate the area of the yard in square meters.
The total amount Alex paid is $8112, and the rate is $12 per square meter.

\[
\text{Area} = \frac{\text{Total amount paid}}{\text{Rate per square meter}} = \frac{8112}{12} = 676 \, \text{square meters}
\]

### Step 2: Find the side length of the square yard.
Since the yard is square-shaped, the area of a square is given by the formula:

\[
\text{Area} = \text{side}^2
\]

We know the area is 676 square meters, so:

\[
\text{side}^2 = 676
\]

Taking the square root of both sides:

\[
\text{side} = \sqrt{676} = 26 \, \text{meters}
\]

Thus, the length of one side of the yard is **26 meters**.

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Do you want more details or have any questions? Here are some related questions you might find interesting:

1. What if the rate was $15 per square meter? How would that change the answer?
2. How would you calculate the area if the yard was rectangular instead of square?
3. How much would Alex pay if the yard were 30 meters on each side?
4. What is the perimeter of the yard if its side is 26 meters?
5. How would you compute the diagonal of the yard?

**Tip:** When dealing with square areas, always remember the relationship between the side length and the area (side length squared equals the area).

Alex paid someone $8112 to mow his square yard at the rate of $12 per square meter. What is the length of one side of the yard?

Learn how to calculate the side length of a square yard based on a total cost of $8112 at a rate of $12 per square meter. This step-by-step solution covers basic algebra and area concepts, suitable for students in Grades 6-8.

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