The perimeter of the triangle OAB is 59 cm. The side OA is 25 cm, and the difference between

The perimeter of the triangle OAB is 59 cm. The side OA is 25 cm, and the difference between the sides OB and AB is 16 cm. Find the sides OB and AB

The perimeter of any triangle is equal to the sum of the lengths of all three sides of this triangle.

According to the condition of the problem, the perimeter P of the triangle OAB is 59 cm, and the length of the side OA is 25 cm, therefore the sum of the lengths of the sides OB and AB is:

| OB | + | AB | = P – | OA | = 59 – 25 = 34 cm.

By the condition of the problem, the difference in the lengths of the sides OB and AB is 16 cm, therefore:

| OB | – | AB | = 16.

Let’s solve the system of equations:

| OB | + | AB | = 34;

| OB | – | AB | = 16.

Adding the first equation with the second, we get:

| OB | + | AB | + | OB | – | AB | = 34 + 16;

2 * | OB | = 50;

| OB | = 50/2;

| OB | = 25 cm.

Subtracting the second equation from the first, we get:

| OB | + | AB | – | OB | + | AB | = 34 – 16;

2 * | AB | = 18;

| AB | = 18/2;

| AB | = 9 cm.

Answer: | OB | = 25 cm, | AB | = 9 cm.