How do i post the answer hence i don't the answer .In geometry.an equalateral triangle has the length of it's sides given as (y + 3)cm, (2y - x)cm and (4x + 3). Find the (a) value of x and y, (b) perimeter of the triangle (c) altitude of the triangle to the nearest whole number.
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5x(8x+9)
To solve this problem, we follow these steps:
(a) To find the values of x and y, we will set up equations based on the given information and then solve for x and y.
Since we know that an equilateral triangle has all sides equal, we can set up the following equation:
y + 3 = 2y - x = 4x + 3
Now, we can solve this equation to find the values of x and y. We will equate each pair of sides in the equation above and solve for x and y.
Equating sides 1 and 2:
y + 3 = 2y - x
Rearranging the equation:
x = 2y - (y + 3)
x = 2y - y - 3
x = y - 3
Equating sides 2 and 3:
2y - x = 4x + 3
Substituting x = y - 3 into the equation:
2y - (y - 3) = 4(y - 3) + 3
2y - y + 3 = 4y - 12 + 3
y + 3 = 4y - 9
3 - 9 = 4y - y
-6 = 3y
y = -2
Now, substitute the value of y back into the equation x = y - 3:
x = -2 - 3
x = -5
Therefore, the value of x is -5 and the value of y is -2.
(b) To find the perimeter of the triangle, we need to sum up the lengths of all three sides. We can use the given expressions for the sides:
Perimeter = (y + 3) + (2y - x) + (4x + 3)
Substituting the values of x and y we found in part (a):
Perimeter = (-2 + 3) + (2(-2) - (-5)) + (4(-5) + 3)
Perimeter = 1 + (-4 + 5) + (-20 + 3)
Perimeter = 1 + 1 + (-17)
Perimeter = 2 - 17
Perimeter = -15
Therefore, the perimeter of the triangle is -15 cm.
(c) To find the altitude of the triangle, we need to determine the height from one vertex to the opposite side. In an equilateral triangle, the altitude will intersect the opposite side at a right angle, dividing it into two equal segments.
Since we have not been provided with the specific side to which the altitude is drawn, we need to find a general formula to calculate the altitude.
Let's denote the altitude as h.
Using the formula for the area of an equilateral triangle:
Area = (base * height) / 2
Since it is an equilateral triangle, all sides are equal, and the base could be any side. Let's consider side (y + 3) as the base, and h as the corresponding height.
Substituting the values:
(h * (y + 3)) / 2 = (sqrt(3) * (y + 3)^2) / 4
Now, we can solve this equation to find the value of h. However, we need more information about the triangle, such as the area or a specific side, to find an accurate answer for the altitude.
Without additional information, it is not possible to determine the altitude to the nearest whole number.
In summary:
(a) The value of x is -5 and the value of y is -2.
(b) The perimeter of the triangle is -15 cm.
(c) Without additional information, it is not possible to determine the altitude to the nearest whole number.