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marin [14]
4 years ago
5

The length of the shortest side of a right triangle is 8. The lengths of the other two sides are represented by two consecutive

odd integers such that a leg is the first integer and the hypotenuse is the second integer. What are the two integers?
Mathematics
2 answers:
Alexandra [31]4 years ago
7 0

Answer: the 2 integers are 15 and 17

Step-by-step explanation:

Let x represent the hypotenuse of the right angle triangle. Since the hypotenuse and the other leg are odd consecutive integers, then the other leg is x - 2 because x is longer

When a right angle triangle is formed, it means that

Hypotenuse² = opposite side² + adjacent side²

If the shortest side is 8, it means that

x² = (x - 2)² + 8²

x² = x² - 2x - 2x + 4 + 64

x² - x² + 2x + 2x = 68

4x = 68

x = 68/4 = 17

Therefore, the length of the other leg is

x - 2 = 17 - 2 = 15

Gennadij [26K]4 years ago
4 0

Answer:

The two integers are;

x is 15 and

x + 2 is 17

Step-by-step explanation:

The given parameters are;

The length of the shortest side = 8

The length of the other two sides are x and (x + 2) where x is an odd integer and hypotenuse side = x + 2

Therefore, we have;

(x + 2)² = 8² + x²

x² + 4·x + 4 = 8² + x²

x² - x² + 4·x = 8² - 4 = 64 - 4 = 60

4·x = 60

x = 15

Therefore, the hypotenuse side = x + 2 = 15 + 2 = 17

The two integers are thus;

x = 15 and

x + 2 = 17.

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The measures of central tendency for this data set are as follows:

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<h3>How to calculate measures of central tendency?</h3>

In Mathematics, there are three (3) main measures of central tendency and these include the following:

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For the mean, we have:

Mathematically, the mean for this data set would be calculated by using this formula:

Mean = [F(x)]/n

For the total number of data, we have:

F(x) = 0 + 1 + 1 + 1 + 2 + 2 + 3 + 3 + 3 + 3 + 4 + 4 + 4 + 5 + 5 + 5 + 6 + 6 + 6 + 7

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Substituting the parameters into the formula, we have:

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For the median, we have:

First of all, we would order the data from lowest to highest and then determine the median as follows:

Data = {0, 1, 1, 1, 2, 2, 3, 3, 3,} 3, 4, {4, 4, 5, 5, 5, 6, 6, 6, 7}

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<h3>How to calculate the mode?</h3>

A mode refers to the most frequently occurring number in a data set. Thus, the mode for this data set is equal to 3.

In conclusion, a box plot of the measures of central tendency for this data set is shown in the image attached below.

Read more on mean here: brainly.com/question/9550536

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