In the diagram below, AB is parallel to DE . AB =20 inches ,DE=12 inches, and BC=15 inches. what is the of DC?
9 inches
Since we do not have the diagram, we have no idea where C is.
To find the length of DC, we need to use the fact that AB is parallel to DE. This means that the corresponding angles A and D are equal.
Since AB = 20 inches and DE = 12 inches, we know that the ratio of the lengths of AB and DE is equal to the ratio of the lengths of AC and CD.
Therefore, we can set up the following proportion:
AB/DE = AC/CD
Plugging in the given values, we get:
20/12 = 15/CD
To solve for CD, we can cross multiply:
20 * CD = 12 * 15
Simplifying, we get:
20 * CD = 180
Dividing both sides by 20, we find:
CD = 180/20
Simplifying further, we get:
CD = 9 inches
Therefore, the length of DC is 9 inches.
To find the length of DC, we can use the concept of similar triangles. Since AB is parallel to DE, triangle ABC and triangle DEC are similar.
In similar triangles, the corresponding sides are proportional. Therefore, we can set up the following proportion:
AB/DE = BC/DC
Substituting the given values, we have:
20/12 = 15/DC
Now, we can cross-multiply to solve for DC:
20 * DC = 12 * 15
Multiplying both sides, we get:
20DC = 180
Finally, we divide both sides by 20 to find DC:
DC = 180 / 20
Simplifying the fraction, we get:
DC = 9 inches