In equilateral triangle ABC, AB=3x and BC=2x+12. Find the numerical value of the perimeter of triangle ABC.
Since it's an equilateral triangle, AB=BC. 3x=2x+12, solve for x.
In an Equilateral triangle, all 3 sides are equal.
Therefore AB = BC = CA
So, 3x = 2x + 12
Subtract 2x from both sides of the equation
3x - 2x = 2x + 12 - 2x
x = 12
Therefore AB = 3x = 3 x 12 = 36
Perimeter = AB + BC + CA = 3AB = 3 x 36 = 108
To find the numerical value of the perimeter of equilateral triangle ABC, we need to know the value of x.
Since it is an equilateral triangle, all sides are equal. Therefore, AB = BC = AC.
In this case, AB = 3x and BC = 2x + 12.
So, we can set up an equation:
3x = 2x + 12
Subtracting 2x from both sides:
x = 12
Now that we know the value of x, we can find the lengths of the sides:
AB = 3x = 3(12) = 36
BC = 2x + 12 = 2(12) + 12 = 36
AC = AB = BC = 36
Finally, to find the perimeter, we add up the lengths of all sides:
Perimeter = AB + BC + AC = 36 + 36 + 36 = 108
Therefore, the numerical value of the perimeter of triangle ABC is 108.
To find the perimeter of triangle ABC, we need to add up the lengths of all three sides.
Given that AB = 3x and BC = 2x + 12, we need to find the value of x in order to calculate the numerical value of the perimeter.
Since triangle ABC is an equilateral triangle, it means that all three sides are equal in length. Therefore, AB = BC = CA.
So, we can set up an equation: AB = BC.
3x = 2x + 12.
To solve for x, we subtract 2x from both sides: 3x - 2x = 2x + 12 - 2x.
x = 12.
Now that we have the value of x, we can substitute it back into the given expressions to find the lengths of AB and BC.
AB = 3x = 3(12) = 36.
BC = 2x + 12 = 2(12) + 12 = 36.
Since the three sides of the triangle are equal, CA = AB = BC = 36.
To find the perimeter, we add up the lengths of all three sides:
Perimeter = AB + BC + CA = 36 + 36 + 36 = 108.
Therefore, the numerical value of the perimeter of triangle ABC is 108.