Problem:
The perimeter of a triangle is 49 cm. One side is 7cm longer than the other and 5cm shorter than the third. Find the length of each side of the triangle.

Solution:

Let us assume that the length of the shortest side of the triangle is x cm.
Then, the other two sides can be expressed as (x+7) cm and (x+5) cm.

We know that the perimeter of a triangle is the sum of the lengths of its sides. Therefore,

x + (x+7) + (x+5) = 49

Simplifying this equation, we get:

3x + 12 = 49

3x = 37

x = 12.33

Therefore, the length of the sides of the triangle are:

Shortest side = x = 12.33 cm
Second side = x + 7 = 19.33 cm
Third side = x + 5 = 17.33 cm

Verification:

Let's verify if the length of sides satisfies the given conditions:

Shortest side = 12.33 cm
Second side = 19.33 cm
Third side = 17.33 cm

Now, we know that the sum of any two sides of a triangle is always greater than the third side. Let's check if this condition is satisfied:

Shortest side + Second side = 12.33 + 19.33 = 31.66 cm > Third side = 17.33 cm
Shortest side + Third side = 12.33 + 17.33 = 29.66 cm > Second side = 19.33 cm
Second side + Third side = 19.33 + 17.33 = 36.66 cm > Shortest side = 12.33 cm

Therefore, the length of the sides of the triangle satisfies all the given conditions.

Conclusion:

Hence, the length of the sides of the triangle are 12.33 cm, 19.33 cm, and 17.33 cm.

Let's assume one side be xso, one side= x-7and another side= x+5so, x+(x-7)+(x+5)=493x-2=493x=49+23x=51x=51/3x=17so, the sides are17,(17-7),(17+5)17,10,22Hence, the numbers are 17,10 and 22 respectively.