The base of the trapezoid is 16 and 24 cm, and the sides are 15 and 11 cm.

| May 9, 2021 | education

The base of the trapezoid is 16 and 24 cm, and the sides are 15 and 11 cm. How much should each side be lengthened so that they intersect.

Let’s say ABCD is our trapezoid. Its foundations AD = 24; BC = 16. Sides AB = 15; DC = 11. Now we will continue its lateral sides to the intersection at a certain point E.
Note that there are two triangles in the figure: a large AED and a small BEC. Since AD ​​and BC are the bases of the trapezoid, they are parallel. Hence, large AED and small BEC triangles are similar. Let’s find the coefficient of similarity: AD / BC = 24/16 = 3/2 it will give us the ratios of all the corresponding sizes of the sides in our triangles.
We need to find the lengths BC and CE of the sides of the small triangle, for this, using the coefficient already known to us, we write down the equations connecting the lengths of the sides of the large and small triangles and solve them:
(AB + BE) / BE = 3/2; AB / BE = 3 / 2-1; AB / BE = 1/2; BE = 2 * AB; BE = 2 * 15 = 30.
(DC + CE) / CE = 3/2; DC / CE = 3 / 2-1; DC / CE = 1/2; CE = 2 * DC; CE = 2 * 11 = 22.
Answer: The sides of the trapezoid need to be extended by 30 and 22 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.