I need the answers to x & y for #14-18 . helpppp pleaseee

14) The values of x= 7√3 and y= 14

15) The values of x= 16 and y= 16√3

16) The values of x= 3√2 and y= 3√2

17) The values of x= 11 and y= 22

18) The values of z= 24  x= 48/√3 and y= 24/√3

Step-by-step explanation:

The properties of Special Triangles :

For triangle 30° - 60° - 90°,

For triangle 45° - 45° - 90°,

14) The given triangle is 30° - 60° - 90°.

The side opposite to the angle 30° ⇒ a = 7

x is the side opposite to the angle 60° ⇒ a√3 = 7√3

y is the side opposite to the angle 90° ⇒ 2a = 14

15) The given triangle is 30° - 60° - 90°.

The side opposite to the angle 90° ⇒ 2a = 32

⇒ a = 32/2

⇒ a = 16

x is the side opposite to the angle 30° ⇒ a = 16

y is the side opposite to the angle 60° ⇒ a√3 = 16√3

16) The given triangle is 45° - 45° - 90°.

The side opposite to the angle 90° ⇒ a√2 = 6

⇒ a = 6/√2

⇒ a = 3√2

x and y are the sides opposite to 45° ⇒ a

Therefore, x = 3√2 and y = 3√2

17) The given triangle is 30° - 60° - 90°.

The side opposite to the angle 60° ⇒ a√3 = 11√3

⇒ a = 11

x is the side opposite to the angle 30° ⇒ a = 11

y is the side opposite to the angle 90° ⇒ 2a = 22

18) The left half of the triangle is 45° - 45° - 90°.

The side opposite to the angle 90° ⇒ a√2 = 24√2

⇒ a = 24.

z is the side opposite to 45° ⇒ a = 24

The right half of the triangle is 30° - 60° - 90°.

The side opposite to the angle 60° ⇒ a√3 = 24

⇒ a= 24/√3

x is the side opposite to the angle 90° ⇒ 2a = 48/√3

y is the side opposite to the angle 30° ⇒ a = 24/√3

The width is:

And the length is:

Step-by-step explanation:

Recall that the area of a rectangle is given by:

Where w is the width and l is the length.

We are given that the length of a rectangle is four meters longer than the width. Thus:

And we also know that the area of the rectangle is 22 square meteres.

Substitute:

Distribute and isolate the equation:

The equation isn't factorable, so we can instead use the quadratic formula:

In this case, a = 1, b = 4, and c = -22. Substitute:

Evaluate:

Thus, our two solutions are:

Since the width cannot be negative, we can ignore the second solution.

Since the length is four meters longer than the width:

Thus, the dimensions of the rectangle are:

Or, approximately 3.0990 by 7.0990.