# For the manufacture of an equilateral triangle and a pentagon, 56 cm of wire were used.

For the manufacture of an equilateral triangle and a pentagon, 56 cm of wire were used. The lengths of the sides of a triangle and a pentagon are the same. Find the perimeter of a pentagon

1) a + a + a = a · 3 – the sum of the lengths of the sides of an equilateral triangle;

2) a + a + a + a + a = a · 5 – the sum of the lengths of the sides of an equilateral pentagon;

3) Since the lengths of the sides of this equilateral triangle and an equilateral pentagon are equal, it is possible to compose an expression that denotes the length of the wire consumed: (a · 3 + a · 5) = a · 8;

4) Knowing that it took 56 cm of wire to make the figures, we find the size of the side of each of the figures: a = 56: 8 = 7 (cm);

5) Calculate the perimeter of an equilateral pentagon using the formula: P = a · 5 = 7 · 5 = 35 (cm).

Answer: P of the pentagon is 35 cm.

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