Question

The first side of a triangle measures 5 inches less than the second side. The third side is 3 inches more than the first side. The perimeter of the triangle is 17 inches. What is the length of the first side?

Answer 1

The length of the first side of the triangle is determined by setting up an equation using the given relationships between the sides and the perimeter. Solving the equation yields the length of the first side, which is 3 inches.

Step-by-step explanation:

To determine the length of the first side of the triangle, let's denote the second side as x inches. According to the problem, the first side is 5 inches less than the second side, so the first side will be x - 5 inches. The third side is 3 inches more than the first side, which gives us x - 5 + 3, or x - 2 inches. The perimeter of the triangle is the sum of the lengths of its three sides, which is given as 17 inches. So, the equation to calculate the perimeter of the triangle is:

• x + (x - 5) + (x - 2) = 17

Combining like terms gives us:

• 3x - 7 = 17

Adding 7 to both sides:

• 3x = 24

Dividing both sides by 3:

• x = 8

Substituting the value of x into the expression for the first side (x - 5), we find the first side to be:

• 8 - 5 = 3 inches

Therefore, the length of the first side of the triangle is 3 inches.