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3 years ago

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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Step-by-step explanation:

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The answer is below

Step-by-step explanation:

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