The hypotenuse of a right triangle is 16 ft longer than the length of the shorter leg. If the area of this triangle is exactly 1
20 ft², what is the length of the hypotenuse in feet? A. 26B. 32C. 40D. 64E. 80
1 answer:
Answer:
A. 26 ft
Step-by-step explanation:
You might recognize that this triangle is a 5-12-13 triangle scaled up by a factor of 2. If so, you know immediately, that the hypotenuse is 2×13 = 26 feet in length.
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If you're not so lucky, you can write equations involving the lengths of the legs of the triangle. Let those be x and y, with x being the shorter leg. Then the Pythagorean relation tells you ...
x² + y² = (x+16)²
and the area relation tells you ...
120 = (1/2)xy
Using the second equation to write an expression for y, we have ...
y = 240/x
Substituting this into the first equation gives ...
x² + (240/x)² = (x+16)²
(240/x)² = 32x +256 . . . . subtract x²
1800 = x²(x +8) . . . . . . . . .multiply by x²/32
This is a cubic with one real root. It can be solved several ways. I like "graphing" as it is quick and easy. Trial and error also works. The factors of 1800 include 10²·18, so it is clear that x=10 is the solution.
The hypotenuse length is x+16, so is 26 feet.
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The attachment shows the graphical solution of the original two equations. This tells you the legs of the triangle are 10 and 24, so the hypotenuse will be 10+16 = 26. The 10-24-26 triangle is recognizable as a scaled version of the 5-12-13 triangle often used in math problems.
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Answer:
A.The mean would increase.
Step-by-step explanation:
Outliers are numerical values in a data set that are very different from the other values. These values are either too large or too small compared to the others.
Presence of outliers effect the measures of central tendency.
The measures of central tendency are mean, median and mode.
The mean of a data set is a a single numerical value that describes the data set. The median is a numerical values that is the mid-value of the data set. The mode of a data set is the value with the highest frequency.
Effect of outliers on mean, median and mode:
- Mean: If the outlier is a very large value then the mean of the data increases and if it is a small value then the mean decreases.
- Median: The presence of outliers in a data set has a very mild effect on the median of the data.
- Mode: The presence of outliers does not have any effect on the mode.
The mean of the test scores without the outlier is:
*Here <em>n</em> is the number of observations.
So, with the outlier the mean is 86 and without the outlier the mean is 86.9333.
The mean increased.
Since the median cannot be computed without the actual data, no conclusion can be drawn about the median.
Conclusion:
After removing the outlier value of 72 the mean of the test scores increased from 86 to 86.9333.
Thus, the the truer statement will be that when the outlier is removed the mean of the data set increases.