the base of an isosceles triangle is one third the lenght of each congruent sides the perimeter of the triangle is 84 cm how long is the base?
If the base is x
each side is 3 x
the perimeter is x + 3 x + 3 x = 7 x
so
7 x = 84
x = 12
To find the length of the base of an isosceles triangle, you can start by letting the length of each congruent side be represented by "x." According to the given information, the base would then be one-third of x.
Perimeter of a triangle is calculated by adding the lengths of all its sides. For an isosceles triangle, there are two congruent sides and one base. So, the perimeter can be expressed as:
Perimeter = 2 congruent sides + base
Given that the perimeter of the triangle is 84 cm, we can write the equation as:
84 = 2x + (1/3)x
To solve for x, we can simplify the equation:
84 = (6/3)x + (1/3)x
84 = (7/3)x
To isolate x, we can multiply both sides of the equation by the reciprocal of (7/3):
84 * (3/7) = x
(12 * 3) = x
36 = x
So, the length of each congruent side is 36 cm, and the length of the base would be one-third of that:
Base = (1/3) * 36
Base = 12 cm
Therefore, the length of the base of the isosceles triangle is 12 cm.