Question

An equilateral triangle has sides that measure 5 x+3 units and 7 x-5 units. What is the perimeter of the triangle? Explain.

Answer 1

To determine the perimeter of an equilateral triangle with sides described by the expressions 5x + 3 units and 7x - 5 units, we first set these expressions equal to each other, solve for x, then use the resulting length for one side to calculate the perimeter by multiplying by 3.

Step-by-step explanation:

The question concerns the calculation of the perimeter of an equilateral triangle with sides that have expressions representing their lengths. An equilateral triangle is a triangle with all three sides of equal length. Since the expressions for the lengths of the sides are provided as 5x + 3 units and 7x - 5 units, these expressions must be equal, because all sides of an equilateral triangle are the same length.

To find the perimeter, we first need to solve for x by setting the expressions equal to each other:
5x + 3 = 7x - 5.
After solving this equation, we can find the length of each side and then multiply by 3 to get the perimeter.a

Answer 2

To find the perimeter of an equilateral triangle with given side lengths, we need to solve for x and substitute the value back into one of the side lengths. Then, we can find the sum of all three side lengths to determine the perimeter.

Step-by-step explanation:

To find the perimeter of an equilateral triangle, we need to determine the lengths of all three sides. In an equilateral triangle, all three sides are equal in length.

Let's set the lengths of the sides as 5x+3 and 7x-5.

Since the triangle is equilateral, we have the equation 5x+3 = 7x-5.

Solving this equation for x, we get x = 4.

Now, we can substitute the value of x back into one of the side lengths to find the actual side length of the triangle.

Substituting x = 4 into 5x+3, we get 5(4)+3 = 23 units.

The perimeter of the triangle is the sum of all three side lengths.

Therefore, the perimeter is 23 + 23 + 23 = 69 units.