Question

Паралеллограм ABCD имеет сторону AB = 42см. Точка E расположена на стороне BC таким образом, что BE / BC = 5 / 7. Прямая DE пересекает прямую AB в точке F. Чему равна длина BF ? Заранее спасибо!

Answer 1

CD=AB=42см, BE=5X, Bc=7x, CE=2X.

∆BFE≈∆CDE по двум углам : угол BEF=углу CED как вертикальные, угол FBE=углу DCE как накрест лежащие при паралельных AE, CD и секущей BC

BF:CD=BE:CE, BF:42=5X:2X, BF=42•5:2= 105 см

ответ: BF ровна 105 см

Answer 2

Given Information:

We are given a parallelogram ABCD with side AB measuring 42 cm. Point E is located on side BC such that BE/BC = 5/7. Line DE intersects line AB at point F. We need to find the length of BF.

Solution:

To find the length of BF, we can use the concept of similar triangles. Since DE is parallel to BC, we can establish the following similarity relationship:

Triangle BDE ~ Triangle BAC

Using this similarity, we can set up the following proportion:

BE/BA = BD/BC

Substituting the given values, we have:

5/7 = BD/42

To find the value of BD, we can cross-multiply and solve for BD:

BD = (5/7) * 42

Simplifying, we get:

BD = 30 cm

Now, we can use the similarity relationship to find the length of BF:

BF/BA = BD/BC

Substituting the known values, we have:

BF/42 = 30/BC

To find the value of BC, we can use the fact that BE/BC = 5/7:

BE/BC = 5/7

Substituting the known values, we have:

5/7 = BE/BC

Cross-multiplying, we get:

7 * BE = 5 * BC

Simplifying, we have:

BC = (7/5) * BE

Substituting this value of BC in the equation for BF, we have:

BF/42 = 30/((7/5) * BE)

Simplifying, we get:

BF/42 = (30 * 5)/(7 * BE)

Simplifying further, we have:

BF/42 = 150/(7 * BE)

Cross-multiplying, we get:

BF = (150 * 42)/(7 * BE)

Simplifying, we have:

BF = 900/BE

Therefore, the length of BF is 900/BE.

Note: The specific value of BE is not provided in the given information, so we cannot determine the exact length of BF without that information.