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zubka84 [21]
3 years ago
12

Find the value of each variable

Mathematics
1 answer:
ohaa [14]3 years ago
6 0

9514 1404 393

Answer:

  11.  x = 13, y = 13√2

  12.  x = 8, y = 4√3

  13.  x = 14√3, y = 7√3

  14.  x = y = 11√2

  15.  x = 12√2, y = 12, z = 12√3

Step-by-step explanation:

The ratios of side lengths in the "special" triangles are (shortest to longest)

  1 : 1 : √2 . . . . . isosceles right triangle

  1 : √3 : 2 . . . . 30°-60°-90° triangle

These ratios make answering these questions much easier.

__

11. 13 : x : y = 1 : 1 : √2

  x = 13, y = 13√2

__

12. 4 : y : x = 1 : √3 : 2

  x = 8, y = 4√3

__

13. y : 21 : x = 1 : √3 : 2

  y = 21/√3 = 7√3

  x = 14√3

__

14. x : y : 22 = 1 : 1 : √2

  x = 22/√2 = 11√2

  x = y = 11√2

__

15. Let 'a' represent the altitude. Then we have ...

  a : z : 24 = 1 : √3 : 2

  a = 12, z = 12√3

and ...

  a : y : x = 1 : 1 : √2

  y = 12, x = 12√2

_____

<em>Additional comment</em>

It is worth remembering that 1/√n = (√n)/n. This is useful when you have to divide by √2 or √3 in the above problems.

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Answer:

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Step-by-step explanation:

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Answer:

<em>d = 3</em>

Step-by-step explanation:

Coordinate Plane

The image provided shows the four points given:

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It can be clearly seen the length of CD is just the difference of their x-coordinates:

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We can also use the formula of the distance.

Given two points C(x,y) and D(w,z), the distance between them is:

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On a coordinate plane, triangles P Q R and S T U are shown. Triangle P Q R has points (4, 4), (negative 2, 0), (negative 2, 4).
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Answer:

The answer is below

Step-by-step explanation:

Two triangles are said to be similar if their corresponding angles are equal and the corresponding sides are in proportion.

The distance between two points on the coordinate plane is given as:

Distance=\sqrt{(x_2-x_1}^2+(y_2-y_1)^2 \\\\Therefore\ in\ triangle\ PQR:\\\\|QR|=\sqrt{(-2-(-2))^2+(4-0)^2}=4\\\\|PQ|=\sqrt{(-2-4)^2+(0-4)^2}=\sqrt{52}=2\sqrt{13}    \\\\|PR|=\sqrt{(-2-4)^2+(4-4)^2}=6

In triangle STU:

|ST|=\sqrt{(-1-2)^2+(-2-(-4))^2}=\sqrt{13}\\\\|SU|=\sqrt{(-1-2)^2+(-4-(-4))^2}  =3\\\\|TU|=\sqrt{(-1-(-1))^2+(-4-(-2))^2}=2

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Hence:

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