The perimeter of a square and an equilateral triangle add up to 77 cm. Both figures have
sides of the same length. How long is each side?

Length of each side = 11 cm

Solution:

Let a be the side of the square.

Side length of square = Side length of equilateral triangle

Therefore, side length of equilateral triangle = a

Perimeter of the square = Number of sides × side

                                        = 4 × a

Perimeter of the square = 4a

Perimeter of the equilateral triangle = Number of sides × side

                                                            = 3 × a

Perimeter of the equilateral triangle = 3a

Sum of the perimeter of a square and equilateral triangle = 77 cm

⇒ 4a + 3a = 77

⇒ 7a = 77

Divide by 7 on both sides of the equation, we get

⇒ a = 11 cm

Length of each side = 11 cm.

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