An equilateral triangle has a perimeter of 15×3 33×5 feet. what is the length of each side?
The Correct Answer and Explanation is :
To find the length of each side of an equilateral triangle with a given perimeter, we first need to understand the properties of equilateral triangles. An equilateral triangle has three equal sides, meaning that each side is of the same length.
Step 1: Understand the Perimeter
The perimeter ( P ) of an equilateral triangle can be expressed mathematically as:
[
P = 3s
]
where ( s ) is the length of one side. In this case, the problem states that the perimeter is ( 15x^3 + 33x^5 ) feet.
Step 2: Set Up the Equation
From the perimeter formula, we can set up the equation:
[
3s = 15x^3 + 33x^5
]
Step 3: Solve for ( s )
To find ( s ), we need to isolate it on one side of the equation. We can do this by dividing both sides by 3:
[
s = \frac{15x^3 + 33x^5}{3}
]
Step 4: Simplify the Expression
Next, we simplify the right side:
[
s = \frac{15x^3}{3} + \frac{33x^5}{3} = 5x^3 + 11x^5
]
Conclusion
Thus, the length of each side of the equilateral triangle is:
[
s = 5x^3 + 11x^5 \text{ feet}
]
Explanation
This means that each side of the triangle is a polynomial expression in terms of ( x ). The term ( 5x^3 ) indicates that there is a cubic relationship with ( x ), while ( 11x^5 ) indicates a quintic relationship. The total length of each side combines these two expressions, reflecting the contributions of both terms.
By factoring the expression, we can see that ( x ) plays a significant role in determining the specific length of the sides. If ( x ) is given a particular numerical value, we can further evaluate the length of each side in feet.