The middle line 21 cm long divides this trapezoid into two trapeziums, the middle lines

| May 2, 2021 | education

The middle line 21 cm long divides this trapezoid into two trapeziums, the middle lines of which are 2: 5. find the base of this trapezoid.

Let the length of the middle line HP, trapezium KBCM be equal to 2 * X cm, then, by condition, the length of the middle line LE, trapezium AKMD is equal to 5 * M.

The KM segment is the middle line of the LPRE trapezoid, then:

KM = (HP + LE) / 2.

21 = (2 * X + 5 * X) / 2.

7 * X = 42.

X = 42/7 = 6.

HP = 2 * 6 = 12 cm.

LE = 5 * 6 = 30 cm.

From the KBCM trapezoid, we determine the length of the BC base.

НР = (ВС + КМ) / 2.

12 = (BC + 21) / 2.

BC = 24 – 21 = 3 cm.

From the trapezoid AKMD we determine the length of the base AD.

LE = (CD + KM) / 2.

30 = (CD + 21) / 2.

СD = 60 – 21 = 39 cm.

Answer: The bases of the trapezoid are 3 cm and 39 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.