trapezoid abfe is similar to trapezoid efcd. a 3 b
e 4.5 f
d c
What is the length of ___?
DC
I need an answer
To find the length of DC in trapezoid EFCD, we can use the concept of similarity. Since trapezoid ABFE is similar to trapezoid EFCD, the corresponding sides are proportional.
Let's denote the length of AB as x and the length of EF as y.
In trapezoid ABFE, we can see that the length of AB is 3 units, and the length of EF is 4.5 units.
Using these values, we can set up a proportion to determine the ratio between the corresponding sides:
AB / EF = x / y
Solving the proportion:
3 / 4.5 = x / y
Now, we want to find the length of DC, which corresponds to the length of AB. We already know that the length of AB is 3 units.
Using the ratio we found, we can substitute the values into the proportion:
3 / 4.5 = 3 / y
Cross-multiplying:
3y = 4.5 * 3
3y = 13.5
Divide both sides by 3:
y = 13.5 / 3
y = 4.5
Therefore, the length of DC in trapezoid EFCD is also 4.5 units.