An isosceles triangle has a perimeter of 9y-15m.what is the length of each of the two equal sides, if the third sides is 3y-7
let each of the equal sides be x
then:
x + x + 3y-7 = 9y - 15
2x = 6y - 8
x = 3y - 4
but the sum of any two sides of a triangle must be greater than the 3rd side.
2x > 3y - 7 , x + 3y - 7 > x
2x +7 > 3y and 3y > 7
y < (2x+7)/3 and y > 7/3
no unique solution:
e.g. let y = 3, then x = 5, sides are 5, 5, 2
let y = 4, then x = 8 , sides are 8, 8, 5
let y = 5, then x = 11 sides are 11, 11, 8
let y = 6, then x = 14, sides are 14, 14, 11
..
let y = 20 , then x = 56, sides are 56, 56, 53
notice that the base is always 3 units less than each of the equal sides, and eventually the triangle will approach the shape of an equilateral triangle.
e.g let y = 5000 , then x = 14996, sides are 14996, 14996, and 14993
To find the length of each of the two equal sides, we need to set up an equation using the perimeter.
Perimeter of a triangle = sum of all sides
In an isosceles triangle, two sides are equal. Let's say the length of each equal side is 'x' and the length of the third side is '3y - 7'.
According to the given information, the perimeter is 9y - 15m. So, we can set up the equation:
x + x + (3y - 7) = 9y - 15
Now we can solve for 'x', which will give us the length of each equal side.
2x + 3y - 7 = 9y - 15
2x = 9y - 15 - 3y + 7
2x = 6y - 8
Dividing both sides by 2:
x = (6y - 8)/2
Simplifying:
x = 3y - 4
Therefore, the length of each of the two equal sides is 3y - 4.
To find the length of each of the two equal sides of an isosceles triangle, we need to consider the perimeter and the length of the third side.
In this case, the perimeter is given as 9y - 15m and the length of the third side is given as 3y - 7.
For an isosceles triangle, the two equal sides will have the same length. Let's call this length 'x'.
To find 'x', we can set up an equation based on the perimeter:
Perimeter = Sum of all three sides
So, we have:
2x + (3y - 7) = 9y - 15m
Now, we can solve this equation to find the value of 'x'.
First, let's simplify the equation by combining like terms:
2x + 3y - 7 = 9y - 15
Next, let's isolate 'x' by moving the variables to one side of the equation and the constants to the other side:
2x = 9y - 15 - 3y + 7
Simplifying further:
2x = 6y - 8
Now, divide both sides of the equation by 2 to solve for 'x':
x = (6y - 8) / 2
Finally, simplify the expression:
x = 3y - 4
Therefore, the length of each of the two equal sides of the isosceles triangle is 3y - 4.