In a trapezoid the lengths of bases are 11 and 18. the lengths of legs are 3 and 7. the extensions of the legs meet at some point. find the length of segments between this point and the vertices of the greater base.

The length of segments between this point and the vertices of greater base are and 18.

Step-by-step explanation:

Let ABCD is the trapezoid, ( shown in below diagram)

In which AB is the greater base and AB = 18 DC= 11, AD= 3 and BC = 7

Let P is the point where The extended legs meet,

So, according to the question, we have to find out : AP and BP

In Δ APB and Δ DPC,

∠ DPC ≅ ∠APB ( reflexive)

∠ PDC ≅ ∠ PAB    ( By alternative interior angle theorem)

And, ∠ PCD ≅ ∠ PBA  ( By alternative interior angle theorem)

Therefore, By AAA similarity postulate,

Let, DP =x

⇒

⇒  33 +11x = 18x

⇒ x = 33/7=

Thus, PD=

But, AP= PD + DA

AP=

Now, let PC =y,

⇒

⇒ 77 + 11y = 18y

⇒ y = 77/7 = 11

Thus, PC= 11

But, PB= PC + CB

PB= 11+7 = 18

its the fourth option

answer: 0.26

i used the calculator on google