In an isosceles triangle, the length of one of the equal side is four less than triple the length of the base. Find length of the base of the triangle if the perimeter of triangle is 55 cm.
side = 3b-4
base = b
side = 3b-4
so
perimeter = 7b -8
7b-8 = 55
7 b = 63
b = 9
To find the length of the base of the isosceles triangle, let's break down the information given step by step:
1. Let's assume that the length of the base of the isosceles triangle is x cm.
2. According to the problem, one of the equal sides is four less than triple the length of the base. Therefore, one of the equal sides can be represented as 3x - 4 cm.
3. Since the isosceles triangle has two equal sides, the total length of these two sides would be 2(3x - 4) cm or 6x - 8 cm.
4. The perimeter of a triangle is calculated by adding the lengths of all three sides. In this case, the perimeter is given as 55 cm.
So, the equation becomes: x + (6x - 8) + (6x - 8) = 55
Let's solve the equation to find the value of x:
x + 6x - 8 + 6x - 8 = 55
13x - 16 = 55
13x = 55 + 16
13x = 71
x = 71 / 13
x ≈ 5.46
Therefore, the length of the base of the isosceles triangle is approximately 5.46 cm.