Questions: 20. Pada gambar di bawah, panjang EF adalah .... * A. 6,75 cm B. 9 cm C. 10,5 cm D. 10,8 cm

Solution Steps

We are given a trapezoid ABCD with AB = 18 cm, CD = 6 cm, AE = 5 cm, and DE = 3 cm. We are asked to find the length of EF.

Since EF is parallel to AB and CD, we can set up a proportion using the similar triangles ADE and ABC:

DE / AB = AE / AC

and

EF / AB = CE / AC

First, find the length of AC. Since AE = 5cm and AC = AE + CE, substituting the first proportion into the second one to eliminate AC, we get:

EF / AB = (AC - AE) / AC
EF / AB = 1 - AE/AC
EF / AB = 1 - DE / AB
EF = AB - AB * (DE / AB)
EF = AB - DE

Substitute the values AB = 18 cm and DE = 3 cm:

EF = 18 cm - 3 cm = 15 cm

However, we are looking for EF, and EF + FC = CD. In this case, the length of EF is calculated by:

EF/AB = CE/AC
EF/18 = (AC-AE)/AC
EF = 18 (1 - 5/AC)

The question should have mentioned that the point F lies on BC so the triangles ABC, EFC, and ADE are similar.

AE/AC = DE/BC = EF/AB
5/AC = 3/BC = EF/18

5 + EC/5+EC+AE = DE/BC
EC = AE (BC - DE)/DE
EC = 5*(BC-3)/3

EF = AB*CE/AC
   = 18 * ((5/3)*(BC-3))/BC

We can also calculate AC in terms of x where x is equal to BC and find the exact value of BC.

AC^2 = 5^2+BC^2 = AE^2+EC^2+2*AE*EC
AC^2 = 25 + x^2
AD^2= 3^2 + 5^2
AD= sqrt(34)

AC^2 - BC^2=25

Final Answer: