Question

Look at the figure below:

Triangle ABC is a right triangle with angle ABC equal to 90 degrees. The length of AC is 7 units and the length of AB is 4 units. D is a point above C. Triangle ADC is a right triangle with angle DAC equal to 90 degrees and DC parallel to AB.

What is the length, in units, of segment CD? (5 points)

5.50
12.25
8
14

Answer 1

Using the Pythagorean Theorem and similarity of triangles, it is found that the length of segment CD is of 8 units.

What is the Pythagorean Theorem?

The Pythagorean Theorem relates the length of the legs $l_1$ and $l_2$ of a right triangle with the length of the hypotenuse h, according to the following equation:

$h^2 = l_1^2 + l_2^2$

First, we find the length of segment BC, which is one leg of a triangle with other leg 4 and hypotenuse 7, hence:

l² + 4² = 7²

l² = 33

l = sqrt(33)

l = 5.74 units.

Then we apply the similarity of triangles to find the length of segment CD, as follows:

• The side of length 5.74 is equivalent to the side of length 7.

• The side of length 7 is equivalent to the side of length x, which is CD.

Hence:

5.74/7 = 7/CD

Applying cross multiplication:

5.74CD = 49

CD = 49/5.74

CD = 8 units.

More can be learned about the Pythagorean Theorem at https://brainly.com/question/654982

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