Question

Look at the figure below: What is the length, in units,
of segment CD?

A: 5.50

B: 12.25

C: 8

D: 14

Answer 1

Answer: 12.25

Step-by-step explanation: The two triangles are proportional. So you find that scale factor that make 4 become 7 which is 1.75 : 1. Multiply 7 × 1.75 = 12.25

Answer 2

The length of the segment CD is 8 units and this can be determined by using the similar triangle property and the Pythagorean theorem.

Given :

• The length of AC = 7 units
• The length of AB = 4 units
• Angle ABC = 90 degrees
• Angle DAC = 90 degrees

The following steps can be used in order to determine the length of the segment CD:

Step 1 - First, determine the length of BC by using the Pythagorean theorem.

$\rm AC^2 = BC^2+AB^2$

Step 2 - Now, substitute the known values in the above expression.

$\rm 7^2 = BC^2+4^2$

$\rm BC=\sqrt{49-16}$

$\rm BC = \sqrt{33}$

Step 3  - Now, apply the similar triangle property, that is:

$\rm \dfrac{BC}{AC}=\dfrac{AC}{CD}$

Step 4 - Substitute the values of the known terms in the above expression.

$\rm \dfrac{\sqrt{33} }{7}=\dfrac{7}{CD}$

$\rm CD=\dfrac{49}{\sqrt{33} }$

CD = 8 (approximately)

Therefore, the correct option is C).

For more information, refer to the link given below:

https://brainly.com/question/25277954