ONe of the equal sides of an isosceles triangle is 3m less than twice its base. the perimeter is 44m. find the lengths of the sides.
i need help with getting the forumula for this problem
thanks
base = b
side = 2b -3
b + 2(2b-3) = 44
lalalal ala la la i don't get how u solve it tho!
Let's start by defining the variables for this problem.
Let's assume that the base of the triangle is x meters.
According to the problem, one of the equal sides is 3 meters less than twice the base. So, this side can be represented as 2x - 3 meters.
Since it's an isosceles triangle, the other equal side will also have the same length as 2x - 3 meters.
To find the perimeter, we can use the formula: Perimeter = sum of all sides.
Here, the perimeter is given as 44 meters. So, we can set up the equation:
Perimeter = base + side1 + side2
44 = x + (2x - 3) + (2x - 3)
Now, we can solve this equation to find the value of x.
44 = x + 2x - 3 + 2x - 3
44 = 5x - 6 + 2x
44 = 7x - 6
7x = 44 + 6
7x = 50
x = 50 / 7
x ≈ 7.14
So, the base of the triangle is approximately 7.14 meters.
To find the lengths of the equal sides, we can substitute the value of x back into the expressions we derived earlier.
One equal side = 2x - 3 ≈ 2(7.14) - 3
≈ 14.29 - 3
≈ 11.29 meters
The other equal side will also have the same length, so it is also approximately 11.29 meters.
Therefore, the lengths of the sides of the triangle are approximately:
Base: 7.14 meters
Equal sides: 11.29 meters
To find the lengths of the sides of the isosceles triangle, we can use the properties and relationships of the sides in an isosceles triangle.
Let's start by assigning variables to the lengths of the triangle's sides. Let the base of the triangle be represented by "x" meters. Since it is mentioned in the problem that one of the equal sides is 3 meters less than twice the base, we can express the length of one of the equal sides as "2x - 3" meters.
Since it's an isosceles triangle, the other equal side will have the same length, so we can also represent it as "2x - 3" meters.
Now, we can set up an equation using the perimeter of the triangle:
Perimeter = Sum of all three sides
44m = x + (2x - 3) + (2x - 3)
Simplifying the equation:
44m = x + 2x - 3 + 2x - 3
Combine like terms:
44m = 5x - 6
Add 6 to both sides of the equation:
44m + 6 = 5x - 6 + 6
44m + 6 = 5x
Subtract 6 from both sides of the equation:
44m = 5x - 6
Now, we can solve for "x" by isolating it:
Divide both sides of the equation by 5:
44m/5 = (5x - 6)/5
8.8m = x - 1.2
Now, we have the value of x.
To find the lengths of the equal sides, substitute x back into the expressions for the equal sides:
Equal side = 2x - 3
Equal side = 2(8.8) - 3
Equal side = 17.6 - 3
Equal side = 14.6
Therefore, the lengths of the sides of the isosceles triangle are: 8.8m, 8.8m, and 14.6m.