# Triangle ABC and MBN shown in the drawing are equilateral. The perimeter of triangle ABC is 15 CM and the perimeter

September 15, 2021 | education

| **Triangle ABC and MBN shown in the drawing are equilateral. The perimeter of triangle ABC is 15 CM and the perimeter of triangle MBN is 9 cm. Find the perimeter of quadrilateral amnc.**

Since, by condition, the triangles ABC and BMN are equilateral, and their perimeters, respectively, are equal to 15 cm and 9 cm, it is possible to determine the sides of the triangles.

AB = BC = AC = Ravs / 3 = 15/3 = 5 cm.

AM = MN = BN = 9/3 = 3 cm.

Let us determine the lengths of the segments AM and CN.

AM = AB – BM = 5 – 3 = 2 cm.

CN = BC – BN = 5 – 3 = 2 cm.

Let’s define the perimeter of the AMNC quadrangle.

Pamnc = AM + MN + CN + AC = 2 + 3 + 2 + 5 = 12 cm.

Answer: The perimeter of the quadrangle is 12 cm.

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