9514 1404 393
Answer:
A- Triangle 2: {8, 15, 17}
Step-by-step explanation:
You may recognize that the triple of choice A is a Pythagorean triple, so can be the side lengths of a right triangle.
Checking the numbers can be done nicely by a graphing calculator or spreadsheet to help avoid the tedium of doing it "by hand".
The basic idea is that the triangle will be a right triangle if the sum of the squares of the shorter sides is the square of the longer side.
Answer:
(C) 3 kg is the maximum possible weight of the lightest box
Step-by-step explanation:
given data is:
so since we know that the median is 9 and the total boxes are 3. We already know the weight of one of the three boxes.
so we can think of the sum of the three weights in ascending order as: A+9+B.
here A and B are the unknown weights of the remaining two boxes.
mean = (sum of all weights)/(number of boxes)
put all the known values in the formula
and rearrange the formula so one of A and B as the subject.
now you can use the given values in the Multiple choices from the question and find the maximum value. try each value to be equal to B, so you can find A.
but you need to be smart about it, and keep in mind that the only one of the value of A and B should be greater than the median i.e. 9, or else that will rearrange the way we have set up our boxes:: A + 9 + B (ascending order).
here, no value is greater than the median: 3+9+7 (not ascending)
here no value is greater than the median: 4+9+8 (not ascending)
here, one of the boxes is equal to the median: 3+9+9 (ascending)
you see a pattern here, the value of A is increasing, thus B is decreasing.
here, you can realize that B = 2 is not correct since this is not maximum possible weight of the lightest box: 2+9+10 (ascending, but the weight of the lightest box is not maximum possible)
Since, we want maximum possible weight for the lightest box, that is only possible when B = 3 (maximum possible)
