An isosceles triangle is a triangle in which the sides are equal:
AB = BC.
The perimeter of a triangle is the sum of the lengths of its sides:
P = AB + BC + AC.
In the first case, suppose the sides are 8 cm smaller than the base.
Thus, we express:
x is the length of the sides AB and BC;
x + 8 is the length of the AC base;
x + x + x + 8 = 44;
x + x + x = 44 – 8;
3x = 36;
x = 36/3 = 12;
AB = BC = 12 cm;
AC = 12 + 8 = 20 cm.
In the second case, suppose the base is 8 cm smaller than the sides.
Based on this, we express:
x is the length of the base of the speaker;
x + 8 – the length of the sides AB and BC;
x + x + 8 + x + 8 = 44;
x + x + x = 44 – 8 – 8;
3x = 28;
x = 28/3 = 9.3 cm;
AC = 9.33 cm;
AB = BC = 9.33 + 8 = 17.33 cm.
Answer: in the first case AB and BC are equal to 12 cm, AC is equal to 20 cm; in the second case AB and BC are equal to 17.33 cm, AC is equal to 9.33 cm.
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