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Dimas [21]
3 years ago
14

Determine if the side lengths could form a triangle. Use an inequality to prove your answer.

Mathematics
1 answer:
podryga [215]3 years ago
7 0

9514 1404 393

Answer:

  a) no

  b) yes

  c) maybe (no)

Step-by-step explanation:

There are two versions of the triangle inequality. One requires ...

  a + b > c

for any triple of side measures a, b, c.

The other allows ...

  a + b ≥ c

which admits "triangles" that have zero height and look like line segments.

Most questions asking "do these lengths form a triangle" are concerned with the "greater than" case, and disallow the "or equal to" case.

__

a)

  16+21=37\ngtr39\qquad\text{not a triangle}

b)

  27+34=61>58\qquad\text{could be a triangle}

c)

  9+29=38\ge38\qquad\text{could be a triangle if "equal to" is allowed}

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3 years ago
Alistair has a rectangular picture measuring 8 inches by 7 inches. He makes a frame for picture. The area of the frame is 34 squ
egoroff_w [7]
Although the question is not given,I can infere that you need to know the value of x, that is the widht of the frame.

Note that the dimensions of the rectangle covered by the frame are:

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While the area of the picture is 8 in * 7 in = 56 in^2.

Then, you can state that the area of just the frame meets this equation:

area of the frame = area of the whole figure - area of the picture

34 = (8+2x)(7+2x) - 56

Now solve the equation, starting by expanding the product of the two parenthesis:

8*7 + 16x + 14x + 4x^2 - 56 = 34

4x^2 + 30x + 56 - 56 - 34 = 0

4x^2 + 30x - 34 = 0

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Factor: (2x - 2)(x + 17/2) = 0

=> 2x - 2 = 0 => x = 1, and x + 17/2 = 0 => x = - 17/2.

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Answer: the widht of the frame is 1 inch.

You can check: (8 + 2) (7 + 2) = (10)(9) = 90 = area of picture + the frame.

90 - 56 = 34 which is the area of the frame.
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Answer:

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Step-by-step explanation:

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Answer:

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Step-by-step explanation:

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