The perimeter of a triangle is 40 inches. The second side exceeds twice the first day by 1 inch and the third side is 2 inches less than the second side. Find the length of each side of the triangle.
Let's assume that the first side of the triangle is x inches.
According to the problem, the second side exceeds twice the first side by 1 inch. So, the second side would be 2x+1 inches.
Similarly, the third side is 2 inches less than the second side, which means it would be 2x+1-2 = 2x-1 inches.
The perimeter of the triangle will be the sum of the lengths of all three sides:
x + (2x+1) + (2x-1) = 40 inches
Simplifying the equation:
5x = 40
Dividing both sides by 5:
x = 8
So, the first side of the triangle is 8 inches.
The second side would be 2x+1 = 2(8)+1 = 17 inches.
And the third side would be 2x-1 = 2(8)-1 = 15 inches.
Therefore, the length of each side of the triangle is 8 inches, 17 inches, and 15 inches.
Let's denote the lengths of the three sides of the triangle as follows:
First side: x inches
Second side: 2x + 1 inches
Third side: (2x + 1) - 2 inches
The perimeter of a triangle is the sum of the lengths of its sides.
Using this information, we can set up the equation:
Perimeter = 40 inches
x + (2x + 1) + ((2x + 1) - 2) = 40
Simplifying the equation:
x + 2x + 1 + 2x + 1 - 2 = 40
5x = 40
x = 8
Therefore, the lengths of the sides of the triangle are:
First side: x = 8 inches
Second side: 2x + 1 = 2(8) + 1 = 17 inches
Third side: (2x + 1) - 2 = 17 - 2 = 15 inches
So, the lengths of the sides of the triangle are 8 inches, 17 inches, and 15 inches.
To solve this problem, let's break it down step by step.
Step 1: Define the variables
Let's assume that the length of the first side of the triangle is "x" inches.
Step 2: Determine the length of the second side
According to the problem, the second side exceeds twice the length of the first side by 1 inch. So the length of the second side would be 2x + 1 inches.
Step 3: Determine the length of the third side
The problem states that the third side is 2 inches less than the second side. Therefore, the length of the third side would be (2x + 1) - 2 inches, which simplifies to 2x - 1 inches.
Step 4: Write the equation for the perimeter
The perimeter of a triangle is the sum of its three sides. So we can write the equation as:
x + (2x + 1) + (2x - 1) = 40
Step 5: Solve the equation
Combine like terms:
x + 2x + 2x + 1 - 1 = 40
5x = 40
x = 8
Step 6: Calculate the lengths of the sides
Now that we know x = 8, we can substitute this value back into the expressions for the second and third sides:
Second side: 2x + 1 = 2(8) + 1 = 17 inches
Third side: 2x - 1 = 2(8) - 1 = 15 inches
So the length of each side of the triangle is:
First side: 8 inches
Second side: 17 inches
Third side: 15 inches