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Chapter 9: Problem 477

The perimeter of an equilateral triangle is 145 feet. Find the length of each side.

Short Answer

Expert verified
Each side is approximately 48.33 feet.

Step by step solution

01

Understand the Problem

The problem provides the perimeter of an equilateral triangle and asks to find the length of each side. An equilateral triangle has all three sides of equal length.
02

Express the Perimeter Formula

For an equilateral triangle, the perimeter is the sum of all three sides. Let the length of each side be denoted as 's'. Thus, the perimeter is given by the formula: \( P = 3s \)
03

Substitute the Given Perimeter

The problem states that the perimeter is 145 feet. Substitute this value into the perimeter formula: \( 145 = 3s \)
04

Solve for the Side Length

To find the value of 's', divide both sides of the equation by 3: \[ s = \frac{145}{3} \]
05

Simplify the Division

Perform the division to get the length of each side: \[ s = 48.33 \text{ feet} \] (rounded to 2 decimal places)

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Equilateral Triangle
An equilateral triangle is a special type of triangle where all three sides are equal in length. This means that not only are the sides the same length, but all three internal angles are also equal, each being 60 degrees. Understanding this property is crucial for solving problems related to equilateral triangles. For instance, knowing that all sides are equal makes it straightforward to calculate the perimeter if one side length is known, or vice versa.
Perimeter Formula
The perimeter of a shape is the total distance around its edges. For an equilateral triangle, calculating the perimeter is particularly simple. If each side is denoted as \( s \), then the perimeter \( P \) is given by the formula:
\[ P = 3s \]
This formula means you just need to multiply the length of one side by three to find the total perimeter. This simplicity is due to the fact that all sides of an equilateral triangle are identical in length.
Solving Equations
In math, solving equations is a fundamental skill. Let's break down how to apply this to our equilateral triangle problem:
  • Start with the equation derived from the perimeter formula: \( P = 3s \).
  • If the perimeter (\( P \)) is given as 145 feet, we substitute this value into the equation: \( 145 = 3s \).
  • Next, isolate \( s \) by dividing both sides of the equation by 3: \( s = \frac{145}{3} \).
  • Perform the division. The answer is approximately 48.33 feet (rounded to two decimal places).

Always remember that accurate calculations and clear expression of each step are essential when solving equations. Practice will make these steps second nature.

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Most popular questions from this chapter

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