The sides of a triangle are three consecutive odd integers. The perimeter of the triangle is 39 inches. What is the length of each of the three sides?
a polymorph is the persistent occurrence of different ppeanc nes ofir a particular trait oin aspecie s aal humans have solight differencew sin their geontyues
x+(x+2)+(x+4)=39
because the first side is x, the next side has to be 2 more than x, and the third 4 more than x
3x+6=39
take it from here
Let's represent the three consecutive odd integers as x, x+2, and x+4.
The perimeter of a triangle is the sum of the lengths of its sides. So, the equation for the perimeter can be written as:
x + (x+2) + (x+4) = 39
Now, let's solve this equation:
3x + 6 = 39
3x = 33
x = 11
Now that we have the value of x, we can find the length of each side by substituting x back into the expression:
Side 1: x = 11 inches
Side 2: x+2 = 11+2 = 13 inches
Side 3: x+4 = 11+4 = 15 inches
Therefore, the lengths of the three sides of the triangle are 11 inches, 13 inches, and 15 inches.
To solve this problem, we can set up an algebraic equation based on the given information.
Let's assume the first odd integer is x. Since the sides of the triangle are three consecutive odd integers, the other two sides would be x + 2 and x + 4.
The perimeter of a triangle is the sum of its side lengths. Therefore, we can set up the equation:
x + (x + 2) + (x + 4) = 39
Now, let's solve the equation step by step:
3x + 6 = 39 (Combine like terms)
3x = 39 - 6 (Subtract 6 from both sides)
3x = 33 (Simplify)
x = 33 / 3 (Divide both sides by 3)
x = 11
Now that we have found the value of x, we can substitute it back into the equation to find the lengths of each side:
First side: x = 11 inches
Second side: x + 2 = 11 + 2 = 13 inches
Third side: x + 4 = 11 + 4 = 15 inches
Therefore, the length of each side of the triangle is 11 inches, 13 inches, and 15 inches.