If three sides of a triangle are represented by three consecutive odd numbers and the perimeter is 75cm.Find the length of the sides.
When we're dealing with consecutive numbers representing the sides of a triangle, the average of the perimeter (i.e. perimeter/3) is the middle number. Hence find the other two numbers.
Let's represent the three consecutive odd numbers as (2x-1), (2x+1), and (2x+3), where x is a positive integer.
According to the given information, the perimeter of the triangle is 75 cm. The perimeter of a triangle is the sum of the lengths of its three sides.
So, we can write the equation as:
(2x-1) + (2x+1) + (2x+3) = 75
Simplifying the equation, we get:
6x + 3 = 75
Subtracting 3 from both sides, we get:
6x = 72
Dividing both sides by 6, we get:
x = 12
Now, we can substitute the value of x back into the sides of the triangle:
Side 1 = 2x-1 = 2(12)-1 = 23 cm
Side 2 = 2x+1 = 2(12)+1 = 25 cm
Side 3 = 2x+3 = 2(12)+3 = 27 cm
Therefore, the lengths of the sides of the triangle are 23 cm, 25 cm, and 27 cm.
To find the length of the sides of the triangle, we can use the fact that three consecutive odd numbers can be represented as (2n-1), (2n+1), and (2n+3), where n is an integer.
Let's assume that the three sides of the triangle are (2n-1) cm, (2n+1) cm, and (2n+3) cm.
The perimeter of a triangle is the sum of all its sides. So, we have the equation:
(2n-1) + (2n+1) + (2n+3) = 75
Now, we can solve this equation to find the value of n, and then calculate the lengths of the sides.
2n - 1 + 2n + 1 + 2n + 3 = 75
6n + 3 = 75
6n = 72
n = 12
Now, we can substitute the value of n back into our assumption to find the lengths of the sides:
Side 1: (2n-1) = (2*12-1) = 23 cm
Side 2: (2n+1) = (2*12+1) = 25 cm
Side 3: (2n+3) = (2*12+3) = 27 cm
Therefore, the lengths of the sides of the triangle are 23 cm, 25 cm, and 27 cm.