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Which of the following sets of numbers could represent the three sides of a right triangle?

Which of the following sets of numbers could represent the three sides of a right-example-1

2 Answers

6 votes

Answer:


\{ 45, 60,75\} would form a right angled triangle.

Explanation:

The numbers which are Pythagorean triplet would form a right angled triangle.

Let us suppose that we have three numbers namely
a ,
b and
c , then if sum of squares of two numbers is equal to the square to third number , then the three numbers are said to be Pythagorean triplet. That is ,


\implies a^2 + b^2 = c^2 \\

Also , here ,


\implies c > a \ ; c > b \\

We start by checking the given options one by ,

Option 1 :-

The three numbers are 49 , 64 and 80 . The largest number is 80 , therefore here c = 80 .


\implies a^2 = 49^2 = 2401 \\


\implies b^2 = 64^2 = 4096 \\


\implies c^2 = 80^2 = 6400 \\

Hence here we can see that,


\implies a^2+b^2\\eq c^2 \\

Hence these numbers do not form a right angled triangle.


\rule{200}2

Option 2 :-

Here ,


\implies a^2 = 45^2 = 2025 \\


\implies b^2 = 60^2 = 3600\\


\implies c^2 = 75^2 = 5625\\

Here we can clearly see that,


\implies a^2 + b^2 = c^2 \\

Hence these sets of number would form a right angled triangle.


\rule{200}2

Option 3 :-

Here ,


\implies a^2 = 48^2 = 2304 \\


\implies b^2 = 55^2 = 3025\\


\implies c^2 = 72^2 = 5184 \\

Hence we can see that,


\implies a^2 + b^2 \\eq c^2 \\

So these numbers would not form a right angled triangle.


\rule{200}2

Option 4 :-

Here ,


\implies a^2 = 34^2 = 1156 \\


\implies b^2 = 56^2 = 3136\\


\implies c^2 = 65^2 = 4225 \\

Again here we can see that,


\implies a^2 + b^2 \\eq c^2 \\

So these numbers would not form a right angled triangle.


\rule{200}2

User Tiju John
by
7.2k points
6 votes

Answer:

Explanation:

48 55 and 72 because you divide the numbers to get the number that adds to 90 degress

User Nathan Strutz
by
8.1k points

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