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ABCD is a parallelogram such that AB is parallel to DC and DA parallel to CB. The length of side AB is 20 cm. E is a point between A and B such that the length of AE is 3 cm. F is a point between points D and C. Find the length of DF such that the segment EF divide the parallelogram in two regions with equal areas

Respuesta :

cael
The length of DF will be 17 cm.

Answer:

[tex]\therefore DF=17cm[/tex]

Step-by-step explanation:

The easiest way to solve this, it's by graphing.

By given, we know that

[tex]AB=20cm[/tex], and [tex]AE=3cm[/tex].

By sum of segments, we have

[tex]AE+EB=AB\\3cm+EB=20cm\\EB=20cm-3cm\\EB=17cm[/tex]

Additionally, we know that segment EF divides the parallelogram in two equal areas, that is, in two equal trapezoids, that means their bases are congruent.

So,

[tex]EB=DF[/tex]

[tex]\therefore DF=17cm[/tex]

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