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2 years ago

Please solve the question in the picture

Mathematics

2 answers:

Vanyuwa [196]2 years ago

6 0

Answer:

shortest: 11 inches
longest: 39 inches

Step-by-step explanation:

Given two side lengths for a triangle, the triangle inequality tells you the third side must have a length between the difference and the sum of the given sides.

<h3>A. minimum length</h3>

The difference of the given sides 25 and 15 is ...

25 -15 = 10

The smallest integer greater than 10 is 11.

The third side must be at least 11 inches long.

<h3>B. maximum length</h3>

The sum of the given sides is ...

25 +15 = 40

The largest integer smaller than 40 is 39.

The third side must be at most 39 inches long.

_____

Additional comment

Formally, the triangle inequality tells you that sides a, b, c must satisfy ...

a +b > c and b +c > a and c +a > b

When we're considering the length of third side (c), there are 3 cases to consider. 1) c is shortest; 2) c is between the other lengths; 3) c is longest. Without loss of generality, we can assume a > b.

1) c is shortest:

a+b>c is always true.
b+c>a ⇒ c>a-b (the positive difference)
c+a>b ⇒ c>b-a (the negative difference)

conclusion: c > a-b

2) a > c > b:

a+b>c is always true.
b+c>a ⇒ c>a-b (the positive difference)
c+a>b ⇒ c>b-a (the negative difference)

conclusion: c > a-b

3) c is longest:

a+b>c (the sum)
b+c>a ⇒ c>a-b (the difference will be less than the sum)
c+a>b ⇒ c>b-a (the negative difference will be less than the sum)

conclusion: a -b < c < a+b . . . . . . for a>b

Alexxandr [17]2 years ago

5 0

Answer:

A. 11"

B. 39"

25 - 15 < x < 25 + 15

10 < x < 40

*x = whole number

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3 years ago

Please solve the question in the picture​

Please solve the question in the picture