Final answer:
To find the lengths of the sides of the triangle, we set up equations using the given conditions and solve for side b. We find that side a is 40 meters, side b is 20 meters, and side c is 38 meters.
Step-by-step explanation:
To solve for the lengths of the sides of a triangle with given conditions, we can set up equations using these conditions and solve for the variables representing the sides of the triangle. Let's represent side b as b meters. According to the given conditions, side a is twice side b, so a = 2b. Furthermore, side c is 2 meters shorter than side a, which means c = a - 2 or c = 2b - 2. The perimeter of the triangle is the sum of the three sides, which is 98 meters, so a + b + c = 98.
By substituting the expressions for a and c into the perimeter equation, we get 2b + b + (2b - 2) = 98. Simplifying this equation gives us 5b - 2 = 98. Adding 2 to both sides of the equation results in 5b = 100, and dividing both sides by 5, we find that b = 20. Now that we have the length of side b, we can easily find side a, which is 2 × 20 = 40 meters, and side c, which is 40 - 2 = 38 meters.
In summary, the lengths of the sides of the triangle are as follows: side a is 40 meters, side b is 20 meters, and side c is 38 meters.