An equilateral triangle has sides that measure 5x+3 units and 7x-5 units. What is the perimeter of the triangle?
the two given sides must be equal
7x - 5 = 5x + 3
2x = 8
x = 4
so one side is 5(4)+3 = 23
the perimeter is 3(23) or 69 units
Thank you so much. I got confused when it said equilateral and it gave me two different units.
Ah, the equilateral triangle, the shape that brings symmetry and balance to our lives. Now, to find its perimeter, we need to add up all three sides.
First, let's call the sides of our beloved equilateral triangle "A," "B," and "C." We have the measurements: A = 5x + 3 units and B = 7x - 5 units.
To find the perimeter, we need to add A + B + C (which is equal to A + B + A, since it's an equilateral triangle).
So, the perimeter (P) would be:
P = (5x + 3) + (7x - 5) + (5x + 3).
We can combine like terms:
P = 5x + 3 + 7x - 5 + 5x + 3
P = 5x + 7x + 5x + 3 - 5 + 3
P = 17x + 1.
Therefore, my friend, the perimeter of our equilateral triangle is 17x + 1 units. And you thought triangles were just for pizza slices!
To find the perimeter of an equilateral triangle, we need to know the length of one side. However, in this case, we have two expressions representing the lengths of the sides.
Given that the two sides of the equilateral triangle measure 5x+3 units and 7x-5 units, we can equate these two expressions and solve for x:
5x+3 = 7x-5
To solve for x, let's first get all the x terms on one side of the equation and the constant terms on the other side:
5x - 7x = -5 - 3
-2x = -8
Now, divide both sides of the equation by -2 to solve for x:
x = (-8)/(-2)
x = 4
Now that we have found the value of x, we can substitute it back into one of the expressions to find the length of the sides:
Length of one side = 5x+3 = 5(4)+3 = 20+3 = 23 units
Since an equilateral triangle has all three sides equal, the perimeter of the triangle is given by:
Perimeter = 3 * Length of one side = 3 * 23 = 69 units
Therefore, the perimeter of the equilateral triangle is 69 units.
To find the perimeter of an equilateral triangle, we need to know the length of one of its sides. In this case, we are given two expressions that represent the lengths of the sides: 5x + 3 and 7x - 5.
Since the triangle is equilateral, all three sides have the same length. So, we can set the two given expressions equal to each other:
5x + 3 = 7x - 5
Next, we solve for x. Let's do that step-by-step:
5x + 3 = 7x - 5
5x - 7x = -5 - 3
-2x = -8
x = (-8)/(-2)
x = 4
Now that we have the value of x, we can substitute it back into one of the expressions to find the length of each side. Let's use 5x + 3:
Side length = 5x + 3
Side length = 5(4) + 3
Side length = 20 + 3
Side length = 23 units
So, the length of each side of the equilateral triangle is 23 units. To find the perimeter, we multiply this length by 3 (since there are three sides):
Perimeter = 3 * 23
Perimeter = 69 units
Therefore, the perimeter of the equilateral triangle is 69 units.