In triangle OAB, angle A is equal to angle B. It is known that Ab = 0.6 OA

In triangle OAB, angle A is equal to angle B. It is known that Ab = 0.6 OA and the perimeter of triangle OAB is 54.6 dm. Find the sides of the triangle.

So angle A is equal to angle B, then triangle OAB is isosceles with base AB, then OA = OB.

Since by definition of the perimeter, it is equal to the sum of all sides, we get the equation:

0.6 * OA + 2 * OA = 54.6;

OA = 54.6: 2.6 = 21 dm.

Then:

AB = 0.6 * 21 = 12.6 dm.

Answer: the sides of the triangle are 21 dm, 12.6 dm, 21 dm.