The bases of the trapezoid are 16 cm and 12.8 cm, and the sides are 4.6 cm and 5.4 cm.

| March 19, 2021 | education

The bases of the trapezoid are 16 cm and 12.8 cm, and the sides are 4.6 cm and 5.4 cm. How much should each of the sides be lengthened so that they intersect?

Let us prove that the triangles AOD and BOС are similar.

In triangles, the angle O is common, the angles OAD and OBC are equal as the corresponding angles at the intersection of parallel straight lines BC and AD secant AO. Then the triangles AOD and ВOС are similar in the first sign of similarity – in two angles.

We denote the segments OB through X cm, OC through Y cm, then the segment AO = (4.6 + X), and OC = (5.4 + Y).

Then AD / ВС = AO / ВO.

16 / 12.8 = (4.6 + X) / X.

16 * X = 58.88 + 12.8 * X.

3.2 * X = 58.88.

X = 58.88 / 3.2 = 18.4 cm.

OB = 18.4 cm.

BP / ВС = DO / CO.

16 / 12.8 = (5.4 + Y) / Y.

16 * Y = 69.12 + 12.8 * Y.

3.2 * Y = 69.12.

Y = 21.6 cm.

OС = 21.6 cm.

Answer: The AB side needs to be lengthened by 18.4 cm, the ОС side by 21.6 cm.



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