The perimeter of a triangle is 25 inches. The first side is 6 inches longer than the second side. The third side is 5 inches shorter than twice the sdcond side. Find the length at each side.
second side --- x
first side --- x+6
third side --- 2x-5
x + x+6 + 2x-5 = 25
4x = 24
x = 6
2nd side --- 6
1st side --- 12
3rd side --- 7
Therefore, the length of the second side is 6 inches, the length of the first side is 12 inches, and the length of the third side is 7 inches.
why did you use my answers without showing your own work?
To find the lengths of the sides of the triangle, we can use algebra. Let's assign variables to represent the lengths of the sides.
Let's say the second side is x inches long.
According to the information given, the first side is 6 inches longer than the second side. So, the length of the first side would be x + 6 inches.
The third side is 5 inches shorter than twice the second side. Twice the second side would be 2x, and then 5 inches less would be (2x - 5) inches.
Now, we can use the formula for the perimeter of a triangle: P = a + b + c, where P is the perimeter and a, b, and c are the side lengths.
Given that the perimeter is 25 inches, we can substitute the values we found:
25 = (x + 6) + x + (2x - 5)
Now, solve the equation for x:
25 = x + 6 + x + 2x - 5
25 = 4x + 1
Subtract 1 from both sides of the equation:
24 = 4x
Divide both sides by 4:
6 = x
Now we can substitute the value of x back into the expressions for the lengths of the sides:
First side: x + 6 = 6 + 6 = 12 inches
Second side: x = 6 inches
Third side: 2x - 5 = 2(6) - 5 = 12 - 5 = 7 inches
Therefore, the lengths of the sides of the triangle are 12 inches, 6 inches, and 7 inches.