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?
5.50
12.25
8
14

12.25 units.

Step-by-step explanation:

Look at the figure attached.

Δ ABC is right triangle with ∠ ABC = 90° and AB = 4 units and AC = 7 units.

So, length of BC will be given by BC² = AC² - AB² = 7² - 4² = 33

⇒ BC = √33 = 5.744 units.

Now, AB ║CD and ∠ CAD = 90°

We have to find the length of the CD

Let draw a line from A parallel to BC which intersects CD at E.

So, Δ AED is also a right triangle with ∠ AED = 90°.

Now, CE = AB = 4 units and BC = AE = 5.744 units.

If DE = x units, then from Δ AED we can write AD² = DE² + AE² = x² + 33 (1)

Again, from Δ ACD, AD² = CD² - AC² = (x + 4)² - 7² = (x + 4)² - 49 (2)

Therefore, from equations (1) and (2) we get,  

x² + 33 = (x + 4)² - 49

⇒33 = 8x + 16 - 49

⇒ 8x = 66

⇒ x = 8.25

Therefore, CD = x + 4 = 8.25 + 4 = 12.25 units. (Answer)

step-by-step :