# In an isosceles triangle, the base is 2 times smaller than the lateral side, and the perimeter

In an isosceles triangle, the base is 2 times smaller than the lateral side, and the perimeter is 50 cm. Find the sides of the triangle.

Let ABC be an isosceles triangle, AB = BC – lateral sides, AC – base.
Let’s designate AC as x, then AB and BC will be designated as 2x (according to the condition, the base is 2 times smaller than the lateral side, which means the lateral side is 2 times larger than the base). Then:
AB + BC + AC = 50 cm (by condition);
2x + 2x + x = 50;
5x = 50;
x = 50/5;
x = 10.
AC = x = 10 cm, AB = BC = 2x = 2 * 10 = 20 cm.
Answer: AB = 20 cm, BC = 20 cm, AC = 10 cm.

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