ABCD rectangular trapezoid BC = 2 cm AD = 10 cm AB refers to CD as 3: 5 find the perimeter.

| August 6, 2021 | education

Given: trapezoid, where BC = 2 cm, AD = 10 cm, AB: CD = 3: 5. It is required to determine the perimeter of the trapezoid.
As you know, the perimeter of a trapezoid is the sum of the lengths of all its sides. It is clear that the perimeter P of the trapezoid ABCD is equal to P = AB + BC + CD + AD. Under the conditions of the assignment, BC = 2 cm and AD = 10 cm are known. In order to determine AB and CD, let us lower the height of the trapezoid CE.
It is clear that ΔCED is a right-angled triangle, since CE ⊥ AD. In addition, since this trapezoid is rectangular (∠A = 90 °), the ABCE figure is a rectangle. Therefore, AE = BC = 2 cm and CE = AB.
Then, from the obvious AD = AE + ED, we get ED = AD – AE = 10 cm – 2 cm = 8 cm. The condition for setting AB: CD = 3: 5 is rewritten as follows: CE: CD = 3: 5. According to the main property proportions, 5 * CE = 3 * CD, whence CE = (3/5) * CD.
By the Pythagorean theorem: CD ^ 2 = CE ^ 2 + ED ^ 2 or CD ^ 2 = ((3/5) * CD) ^ 2 + (8 cm) ^ 2 or 25 * CD2 = 9 * CD ^ 2 + 25 * 64 cm2, whence 16 * CD2 = 25 * 64 cm2.
The last equality allows us to assert that CD = 10 cm.Then CE = (3/5) * 10 cm = 6 cm.Therefore, AB = 6 cm.Finally, P = 6 cm + 2 cm + 10 cm + 10 cm = 28 cm.
Answer: 28 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.