The perimeter of an isosceles triangle is 15.6 m. Find the lengths of its sides, if:
The base is 3 m smaller than a leg
length of leg --- x
2x + x-3 = 15.6
solve for x
To find the lengths of the sides of the isosceles triangle, let's represent the length of one leg as x.
According to the given information, the base is 3 m smaller than a leg. So the length of the base can be represented as (x - 3).
Since the triangle is isosceles, it has two congruent sides (legs). Therefore, the perimeter can be determined by adding the lengths of the two legs and the base:
Perimeter = Length of Leg 1 + Length of Leg 2 + Length of Base
15.6 = x + x + (x - 3)
Now, let's solve the equation to find the value of x:
15.6 = 3x - 3
Adding 3 to both sides of the equation:
15.6 + 3 = 3x
18.6 = 3x
Dividing both sides of the equation by 3 to isolate x:
18.6/3 = x
x ≈ 6.2
So the length of one leg of the isosceles triangle is approximately 6.2 m.
To find the length of the base, substitute the value of x back into the equation:
Length of Base = x - 3 = 6.2 - 3 = 3.2
Therefore, the length of the base is approximately 3.2 m.
To summarize, the lengths of the sides of the isosceles triangle are approximately:
Leg 1: 6.2 m
Leg 2: 6.2 m
Base: 3.2 m