The perimeter of an isosceles triangular lot is 47 m. One side is
17 m long. What is the length of each of the two equal sides? I fencing material costs P170 per meter, how much will it cost tr fence the lot?

Let's break down the problem step by step.

### Step 1: Find the length of the two equal sides.

Given:
- The perimeter of the isosceles triangle is 47 meters.
- One of the sides is 17 meters.

In an isosceles triangle, two sides are equal. Let's denote the length of each of the equal sides by \( x \).

The perimeter of the triangle is the sum of all its sides:
\[
x + x + 17 = 47
\]
This simplifies to:
\[
2x + 17 = 47
\]

Now, solve for \( x \):
\[
2x = 47 - 17
\]
\[
2x = 30
\]
\[
x = \frac{30}{2} = 15
\]

So, each of the two equal sides is 15 meters long.

### Step 2: Calculate the cost of fencing the lot.

The total perimeter of the triangle is 47 meters. The cost of fencing is given as \( P170 \) per meter.

Total cost = Perimeter × Cost per meter:
\[
\text{Total cost} = 47 \times 170 = 7990 \text{ PHP}
\]

### Final Answer:
- **The length of each of the two equal sides is 15 meters.**
- **The total cost to fence the lot is 7,990 PHP.**

Would you like to go over any details or have any questions?

### Related Questions:
1. What is the area of the isosceles triangle with the given side lengths?
2. How would the cost change if the price of fencing material increased by 10%?
3. If the triangular lot were to be divided into two smaller triangles, what would be the perimeter of each?
4. What would the perimeter be if the third side was 20 meters instead of 17 meters?
5. How does the perimeter of an isosceles triangle compare to that of an equilateral triangle with the same perimeter?

### Tip:
When solving perimeter problems, always check if the triangle or shape has specific properties, like being isosceles or equilateral, to simplify calculations.

Learn how to calculate the perimeter of an isosceles triangle and determine fencing costs with a detailed step-by-step solution. Given one side length and total perimeter, find the lengths of the equal sides and compute total fencing costs at P170 per meter. Suitable for Grades 7-9.

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