The sides of the equilateral are given in cm. 3x 2,2y-x,y 3. Find x and y and the perimeter of the triangle
Since all the sides are equal, we have
3x 2 = 2y-x
2y-x = y 3
Fix your typos and then solve for x and y. If I assume that your "+" key is not working, then we have
3x+2 = 2y-x
2y-x = y+3
(x,y) = (2,5)
So, the sides are 8 and p=24.
What if they ask you to look for the value of x only
Not clear
To find the values of x and y, we can set up a system of equations based on the given side lengths.
Let's label the sides of the equilateral triangle as a, b, and c, where:
a = 3x + 2
b = 2y - x
c = y + 3
Since it is an equilateral triangle, all three sides are equal. Therefore, we can equate any two sides to find the values of x and y.
Setting sides a and b equal, we have:
3x + 2 = 2y - x
Simplifying the equation, we have:
4x = 2y - 2
Divide by 2:
2x = y - 1
Setting sides b and c equal, we have:
2y - x = y + 3
Simplifying the equation, we have:
y - x = 3
Now we have a system of equations:
2x = y - 1
y - x = 3
From the second equation, we can isolate y:
y = x + 3
Substituting this value of y into the first equation:
2x = (x + 3) - 1
Simplifying the equation, we have:
2x = x + 2
Subtracting x from both sides:
x = 2
Now substituting the value of x back into the equation y = x + 3:
y = 2 + 3
y = 5
So, x = 2 and y = 5.
To find the perimeter of the equilateral triangle, we need to find the value of any side. Let's substitute x = 2 into side a:
a = 3x + 2
a = 3(2) + 2
a = 6 + 2
a = 8
Now we know that all sides are 8 cm. The perimeter (P) of an equilateral triangle is given by P = 3a (where a is the length of each side).
Plugging in the value of a:
P = 3(8)
P = 24 cm
Therefore, the perimeter of the equilateral triangle is 24 cm.