Question

Help!
Find the value of X and simplify completely.

Answer 1

x = 8√3

Explanation:

y /4 = 16/y

y^2 = 64

y = 8

x^2 = 16^2 - 8^2

x^2 = 256 - 64

x^2 = 192

x = √192

x = √(64 * 3)

x = 8√3

Answer 2

x = 8√5

Explanation:

In the figure attached, there are three right angle triangles.

So, by Pythagoras theorem,

y²+ 4² = z²

y² + 16 = z²------(1)

Similarly x² = 16² + y²--------(2)

and (16 + 4)² = x² + z²

20² = x² + z²-------(3)

Now we put the value of z² from equation 1 to equation 3

20² = x² + y² + 16

x² + y² = 400 - 16

x² + y² = 384

y² = 384 - x²------(4)

Now we put the value of y² from equation 4 to equation 2

x² = 16² + 384 - x²

2x² = 256 + 384

2x² = 640

x² = 320

x = 8√5

Therefore x = 8√5 will be the answer.