Question

Please Help!! A.S.A.P!!!

Similarity In Right Triangles, (Solve For X)

A). 10.5

B) 10

C) 20

D)
$6 \sqrt{3}$

Answer 1

Answer:

D)

Step-by-step explanation:

Turn the smaller triangle. You will get similar triangle of 3/(altitude)=(altitude)/9. This means the altitude is 3sqrt3. Now just use the Pythagorean Theorem and get 27+81 or 108. Take the square root of this and you get 6sqrt3 or D).

Answer 2

Answer:

x = 6$\sqrt{3}$

Step-by-step explanation:

As we can see, there are 3 right triangle in the photo

Let y be the altitude of the largest triangle.

Let z be the left side.

• For large triangle:

x² + z² = (9+3)²

<=> x² + z² = 144(1)

• For left sub-triangle

y² + 3² = z² (2)

• For right sub-triangle:

y² + 81 = x²  

<=> y² = x²  - 81 (3)

Substitute (3) and (2) into (1), we have:

x² + z² = 144 (1)

<=> x² + y² + 3²  = 144

<=> x² + (x²  - 81) + 9 =144

<=> 2x² =  216

<=> x² = 108

<=> x = 6$\sqrt{3}$