in the figure, it is given that AB = 21, BC = 14, and AD = 54. find the lenth of CD
What is the figure and where are these segments? (AB, BC, AD, CD) located on this figure?
AD = AB + BC + CD
54 = 21 + 14 + CD
54 = 35 + CD
19 = CD
To find the length of CD, we can use the given information and apply the concept of similar triangles.
First, let's identify the triangles involved in the figure. From the given information, we know that triangle ABC and triangle ACD are similar since they share angle A. This means that their corresponding sides are proportional.
Let x represent the length of CD. Then we have the following proportions:
AB/BC = AD/CD
Substituting the given values, we have:
21/14 = 54/x
To solve for x, we can cross multiply:
21 * x = 14 * 54
Now, let's calculate the right side of this equation:
294x = 756
Dividing both sides of the equation by 294, we find:
x = 756/294
Simplifying the fraction, we get:
x ≈ 2.57
Therefore, the length of CD is approximately 2.57 units.