The perimeter of the rhombus ABCD is 40, the perimeter of the triangle ABD is 32.

| September 16, 2021 | education

The perimeter of the rhombus ABCD is 40, the perimeter of the triangle ABD is 32. Find the perimeter of the triangle ABC.

To solve the problem, consider the figure.

Since all sides of the rhombus are equal to each other, its sides are equal to 40/4 = 10 cm.

Consider a triangle ABD, the perimeter of which is P = 32 cm.

Its side BD is equal to BD = P – AB – AD = 32 – 10 -10 = 12 cm.

Since BD is the diagonal of the rhombus, and they are halved at the intersection point, then BO = BD / 2 = 12/6 = 6 cm.

Consider the triangle AOB and, based on the Pythagorean theorem, find the leg AO.

AO ^ 2 = AB ^ 2 – BO ^ 2 = 100 – 36 = 64.

AO = 8 cm.

Then AC = 2 * AO = 2 * 8 = 16 cm.

The perimeter of the triangle ABC = 10 + 10 + 16 = 36 cm.

Answer: The perimeter of the triangle ABC = 36 cm.



One of the components of a person's success in our time is receiving modern high-quality education, mastering the knowledge, skills and abilities necessary for life in society. A person today needs to study almost all his life, mastering everything new and new, acquiring the necessary professional qualities.