Question

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

Answer 1

`\{ 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`

Answer 2

Explanation:

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