Answer :
* The problem states that the perimeter of a pentagon is 176 cm and provides the lengths of four sides: 27 cm, 36 cm, 48 cm, and 15 cm.
* We set up an equation to represent the perimeter as the sum of all five sides: $27 + 36 + 48 + 15 + x = 176$.
* We calculate the sum of the known sides: $27 + 36 + 48 + 15 = 126$.
* We solve for the unknown side $x$ by subtracting the sum from the total perimeter: $x = 176 - 126 = 50$. The length of the fifth side is $\boxed{50 \text{ cm}}$.
### Explanation
1. Problem Analysis
We are given that the perimeter of a pentagon is 176 cm. We also know the lengths of four of its sides: 27 cm, 36 cm, 48 cm, and 15 cm. Our goal is to find the length of the fifth side.
2. Setting up the Equation
Let's denote the length of the fifth side as $x$. The perimeter of a pentagon is the sum of the lengths of all its five sides. Therefore, we can write the equation:$$27 + 36 + 48 + 15 + x = 176$$
3. Calculating the Sum of Known Sides
First, we need to find the sum of the known side lengths:$$27 + 36 + 48 + 15 = 126$$So, our equation becomes:$$126 + x = 176$$
4. Solving for the Unknown Side
Now, we need to solve for $x$ by subtracting 126 from both sides of the equation:$$x = 176 - 126$$$$x = 50$$Therefore, the length of the fifth side is 50 cm.
5. Final Answer
The length of the fifth side of the pentagon is 50 cm.
### Examples
Understanding perimeters is useful in many real-life situations. For example, if you're building a fence around a pentagon-shaped yard, you need to know the perimeter to determine how much fencing material to buy. Similarly, if you're decorating a pentagonal room with a border, knowing the perimeter helps you calculate the length of the border needed. This concept is also used in designing furniture or creating patterns that fit specific shapes.
* We set up an equation to represent the perimeter as the sum of all five sides: $27 + 36 + 48 + 15 + x = 176$.
* We calculate the sum of the known sides: $27 + 36 + 48 + 15 = 126$.
* We solve for the unknown side $x$ by subtracting the sum from the total perimeter: $x = 176 - 126 = 50$. The length of the fifth side is $\boxed{50 \text{ cm}}$.
### Explanation
1. Problem Analysis
We are given that the perimeter of a pentagon is 176 cm. We also know the lengths of four of its sides: 27 cm, 36 cm, 48 cm, and 15 cm. Our goal is to find the length of the fifth side.
2. Setting up the Equation
Let's denote the length of the fifth side as $x$. The perimeter of a pentagon is the sum of the lengths of all its five sides. Therefore, we can write the equation:$$27 + 36 + 48 + 15 + x = 176$$
3. Calculating the Sum of Known Sides
First, we need to find the sum of the known side lengths:$$27 + 36 + 48 + 15 = 126$$So, our equation becomes:$$126 + x = 176$$
4. Solving for the Unknown Side
Now, we need to solve for $x$ by subtracting 126 from both sides of the equation:$$x = 176 - 126$$$$x = 50$$Therefore, the length of the fifth side is 50 cm.
5. Final Answer
The length of the fifth side of the pentagon is 50 cm.
### Examples
Understanding perimeters is useful in many real-life situations. For example, if you're building a fence around a pentagon-shaped yard, you need to know the perimeter to determine how much fencing material to buy. Similarly, if you're decorating a pentagonal room with a border, knowing the perimeter helps you calculate the length of the border needed. This concept is also used in designing furniture or creating patterns that fit specific shapes.
