If a equileteral triangle has 3 sides in cm x+4, 4x+y, y+2.calculate the length of each sides.
so they are all equal to each other. Go ahead and do it.
4 x + y = y + 2
so
x = 1/2
x+4 = 4 1/2
y+2 = 4 1/2
y = 2 1/2
so
4x + y = 4 1/2 check all sides are 4 1/2
An equilateral triangle is a triangle in which all three sides are equal.
In this case :
x + 4 = 4 x + y = y + 2
x - 4 x + 4 = y
- 3 x + 4 = y
y = - 3 x + 4
4 x + y = y + 2
4 x = y - y + 2
4 x = 2 Divide both sides by 4
x = 2 / 4
x = 1 / 2
y = - 3 x + 4
y = - 3 * 1 / 2 + 4
y = - 3 / 2 + 4
y = - 3 / 2 + 8 / 2
y = 5 / 2
first side:
x + 4 = 1 / 2 + 4 = 1 / 2 + 8 / 2 = 9 / 2 = 4.5 cm
second side :
4 x + y = 4 * 1 / 2 + 5 / 2 = 4 / 2 + 5 / 2 = 9 / 2 = 4.5 cm
third side :
y + 2 = 5 / 2 + 2 = 5 / 2 + 4 / 2 = 9 / 2 = 4.5 cm
To find the length of each side of an equilateral triangle, we can use the fact that all sides of an equilateral triangle are equal in length.
Given that the equilateral triangle has three sides measured in centimeters as x+4, 4x+y, and y+2, we can set up the following equations:
x + 4 = 4x + y
4x + y = y + 2
Solving the first equation for x:
x + 4 = 4x + y
4 - y = 4x - x
4 - y = 3x
x = (4 - y) / 3
Substituting the value of x in the second equation:
4x + y = y + 2
4((4 - y) / 3) + y = y + 2
Simplifying the equation further:
(16 - 4y) / 3 + y = y + 2
16 - 4y + 3y = 3y + 6
Rearranging the equation:
16 - 6 = 3y - 4y + 3y
10 = 2y
y = 5
Substituting the value of y into x:
x = (4 - y) / 3
x = (4 - 5) / 3
x = -1 / 3
Therefore, the length of each side of the equilateral triangle is:
x + 4 = (-1 / 3) + 4 = 11/3 cm
4x + y = (4)(-1 / 3) + 5 = (4/3) + 5 = 19/3 cm
y + 2 = 5 + 2 = 7 cm
Hence, the lengths of the sides of the equilateral triangle are 11/3 cm, 19/3 cm, and 7 cm.