Find the sides of an isosceles triangle if: a) its perimeter is 36 cm and the base is 1.6 of the lateral side;

Find the sides of an isosceles triangle if: a) its perimeter is 36 cm and the base is 1.6 of the lateral side; b) its perimeter is 40 cm, and one of the sides is 12 cm.

Let an isosceles △ ABC be given, in which AB = BC – lateral sides, AC – base.
a) The perimeter of a polygon is the sum of the lengths of all its sides.
In △ ABC:
AB + BC + AC = 36 cm.
Let’s designate sides AB and BC as x, then the base of AC will be equal to 1.6 * x, since the base is 1.6 of the side. Hence:
x + x + 1.6 * x = 36;
3.6 * x = 36;
x = 36/3.6;
x = 10.
Thus, the length of the side side △ ABC AB = BC = x = 10 cm, and the length of the base AC = 1.6 * x = 1.6 * 10 = 16 (cm).
Answer: AB = BC = 10 cm, AC = 16 cm.
b) B △ ABC:
AB + BC + AC = 40 cm.
b. 1) Let AB = BC = 12 cm, then:
12 + 12 + AC = 40;
AC = 40 – 24;
AC = 16 cm.
So AB = BC = 12 cm, AC = 16 cm.
Answer: AB = BC = 12 cm, AC = 16 cm.
b. 2) Let AC = 12 cm, then AB = BC = x:
x + x + 12 = 40;
2 * x = 40 – 12;
2 * x = 28;
x = 28/2;
x = 14.
Thus, AB = BC = x = 14 cm, AC = 12 cm.
Answer: AB = BC = 14 cm, AC = 12 cm.