17 x
3
8
Find the unknown side length, x. Write your answer in simplest radical form.
A 15
B. 5/10
C2/70
D. 4 37

Explanation:

It helps to add point labels. Let's place point A at the very top point of the triangle. Then point B will be at the 90 degree angle. Point C is the far left point. Lastly, point D is on segment BC such that DC = 3.

Since BC = 8 and CA = 17, we can use the pythagorean theorem to get...

(AB)^2 + (BC)^2 = (AC)^2

(AB)^2 + (8)^2 = (17)^2

(AB)^2 + 64 = 289

(AB)^2 = 289-64

(AB)^2 = 225

AB = sqrt(225)

AB = 15

Now focus on triangle ABD and apply the pythagorean theorem again to find side AD

(AB)^2 + (BD)^2 = (AD)^2

AD = sqrt(  (AB)^2 + (BD)^2  )

AD = sqrt(  (AB)^2 + (BC-CD)^2  )

AD = sqrt( (15)^2 + (8-3)^2 )

AD = sqrt(250)

AD = sqrt(25*10)

AD = sqrt(25)*sqrt(10)

AD = 5*sqrt(10) answer is choice B

answer: 4

step-by-step explanation: