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Thepotemich [5.8K]
3 years ago
15

If there are 736 students in a school, prove that at least three students have a birthday on the same day of the year.

Mathematics
1 answer:
serg [7]3 years ago
4 0

Step-by-step explanation:

736 / 365 = 2R6

So even if the first 365 students all have different birthdays, and the next 365 students also all have different birthdays, then there are 2 students for every birthday.  The last 6 students therefore share a birthday with at least 2 other students.  So there are at least 3 students who share a birthday.

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Describe the possible side lengths of the 3rd side of the triangle given the lengths of the 2 other sides?
Sindrei [870]
Heya !

Using a theoram about triangles ,

Given a triangle ∆ABC, the sum of the lengths of any two sides of the triangle is greater than the length of the third side ,

Also , the length of third side always greater than absolute difference of the other two sides ,

Let the third side be x ,

So , x < 9 + 8 and x > 9 - 8
x < 17 and x > 1

Hence , x ∈ [ 2 , 17 ] inch.

Above case is true for any triangle , be it scalene , Isosceles , Right-angled ...

As , for Isosceles , the third side can be 8 or 9 inches ,
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For right angled triangle , we have 2 cases ,

Case 1 : Third side is the hypotenuse
Then , x = √(9²+8²) = √145 = 12.0415 inch.

Case 2 : Third side is not the hypotenuse
Then , x = √(9²-8²) = √17 = 4.1231 inch.

Hope it helps you ! :)
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3 years ago
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10

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Help me out thank you. use the image I have attached.
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3 years ago
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