Question

the lengths of the sides of a triangle are consecutive integers. find the length of the longest side if it is 22 units shorter than the perimeter.

Answer 1

In this problem, we need to find the length of the longest side of a triangle whose sides are consecutive integers and the longest side is 22 units shorter than the perimeter. By assuming the sides as x, x+1, and x+2, and using the given information, we can set up an equation and solve it to find the value of x and the length of the longest side.

Step-by-step explanation:

In this problem, we are given that the lengths of the sides of a triangle are consecutive integers. Let's assume that the three consecutive integers are x, x+1, and x+2 (where x is the smallest side length). We are also given that the longest side is 22 units shorter than the perimeter.

The perimeter of a triangle is the sum of the lengths of its three sides. So, the perimeter can be expressed as x + (x+1) + (x+2). According to the problem, the longest side is 22 units shorter than the perimeter. Therefore, we have the equation: x+2 = (x + (x+1) + (x+2)) - 22.

Simplifying this equation, we get: x + 2 = 3x + 1 - 22. Solving for x, we obtain x = 9.

Therefore, the length of the longest side is x+2 = 9+2 = 11 units.

Answer 2

P=x +(x+1) + (x+2)
P-22 = x+2

P=3x + 3
P= x + 24

Solving: by subtracting the two equations yields 0 = 2x-21 then x = 10.5

Longest side is then x+2 = 12.5