The sides of the trapezoid are 8cm and 1.2dm, and the base is 1.8dm and 24cm by how much the sides

univerkov | September 6, 2021 | education

The sides of the trapezoid are 8cm and 1.2dm, and the base is 1.8dm and 24cm by how much the sides need to be lengthened so that they intersect.

Consider triangles AED and BED. They have a common angle E, and AD is parallel to BC, therefore the triangles are similar.

AE / BE = DE / CE = AD / BC.

AD / BC = 24/18 = 4/3.

AE / BE = 4/3.

3 * AE = 4 * BE

AE = AB + BE = 8 + BE.

3 * (8 + BE) = 4 * BE.

32 + 3 * BE = 4 * BE.

BE = 32 cm.

DE / CE = 4/3.

3 * DE = 4 * CE.

DE = CD + CE = 12 + CE.

3 * (12 + CE) = 4 * CE.

36 + 3 * CE = 4 * CE.

CE = 36 cm.

Answer: The AB side should be increased by 32 cm, and the DC side by 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.