The perimeter of an isosceles triangle is 34 cm, one of the sides is 8 times larger than the other. Find the sides of the triangle.

| February 6, 2021 | education

Let’s consider 2 possible cases.

1) The base of this isosceles triangle is 8 times its lateral side.

Let x denote the length of the lateral side of this triangle. Then the second side will also be x, and the length of the base will be 8x.

However, since the sum of the lengths of the sides of this isosceles triangle, equal to 2x, will be less than the length of the third side, such a triangle cannot exist.

2) The lateral side of this isosceles triangle is 8 times its base.

Let x denote the length of the base of this triangle. Then the lengths of the sides should be 8x.

According to the condition of the problem, the perimeter of this triangle is 34 cm, therefore, we can draw up the following equation:

x + 8x + 8x = 34,

solving which, we get:

17x = 34;

x = 34/17 = 2 cm.

Therefore, the length of the base of the triangle is 2 cm, and the length of the side side is 8 * 2 = 16 cm.

Answer: the length of the base of the triangle is 2 cm, and the length of the lateral side is 16 cm.



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