The two outer corners of the triangle at different vertices are equal. The perimeter of the triangle

| April 29, 2021 | education

The two outer corners of the triangle at different vertices are equal. The perimeter of the triangle is 74 cm, and one of the sides is 16 cm. Find the sides of the triangle.

1. Vertices of triangle A, B, C.

2. According to the condition of the problem, two external angles at different vertices are equal. Suppose the outer angles at the vertices B and C are equal.

The internal angles at the indicated vertices are also equal: ∠В = ∠С. Therefore, the triangle is isosceles. That is, AB = AC.

3. According to the properties of a triangle, the sum of any two of its sides is greater than the third, that is, only the side of the BC can have a length of 16 cm. If the length of each equal sides were equal to 16 cm, then their sum – 32 cm would be less than the length of the third side – 42 cm

(74 cm – 32 cm).

4. We calculate the length of each of the equal sides:

AB = AC = (74 – 16) / 2 = 29 cm.

Answer: AB = AC = 29 cm, BC = 16 cm.



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