Problem 277 - Elementary Algebra

Question

Christa wants to put a fence around her triangular flowerbed. The sides of the flowerbed are six feet, eight feet and 10 feet. How many feet of fencing will she need to enclose her flowerbed?

Step-by-Step Solution

Answer

24 feet

Step 1: Identify the problem

The problem requires the total length of fencing necessary to enclose a triangular flowerbed given the lengths of its sides.

Step 2: Write down the given information

The sides of the triangular flowerbed are given as 6 feet, 8 feet, and 10 feet.

Step 3: Calculate the perimeter of the triangle

To find the total length of fencing needed, calculate the perimeter of the triangle by adding the lengths of all three sides: \[ \text{Perimeter} = 6 \text{ feet} + 8 \text{ feet} + 10 \text{ feet} \]

Step 4: Perform the addition

Add the lengths of the sides together: \[ 6 + 8 + 10 = 24 \text{ feet} \]

Step 5: Write the final answer

The total length of fencing needed to enclose the triangular flowerbed is 24 feet.

Key Concepts

triangular perimeter

To understand how to find the perimeter of a triangle, it's important to grasp the concept of perimeter itself. The perimeter of any shape is the total distance around the shape. For a triangle, this means adding up the lengths of all its three sides.

In our example with Christa's flowerbed, we know the lengths of the three sides: 6 feet, 8 feet, and 10 feet. By summing these lengths, we find the perimeter, which is the total length of the fencing needed.

addition of sides

When calculating the perimeter, the primary task is the addition of the sides. This is done by simply adding the lengths of each side together.

Here's the math from our problem:
We start with the three given lengths of the triangle: 6 feet, 8 feet, and 10 feet.

We then add these numbers together:

• 6 feet + 8 feet = 14 feet
• 14 feet + 10 feet = 24 feet

Thus, the perimeter, or the total length of fencing that Christa needs to enclose her triangular flowerbed, is 24 feet.

elementary algebra geometry

This exercise combines the basic principles of both elementary algebra and geometry.

In elementary algebra, we perform operations such as addition and understand variables. Here, each side of the triangle is treated as a given numerical value or variable. By adding them, we find the total value we need.

In geometry, we often deal with shapes such as triangles, and we need to understand properties like the perimeter. This problem bridges these two areas, showing how they work together.

By practicing such problems, students can strengthen their understanding of how to apply basic algebraic operations to geometric figures to solve practical, real-world problems.