Question

Which of the following measurements represent a right triangle?

1) 3,4,5
2)5,12,14
3)4,√24,8
4)5,7,√74

please help and show ur work!! there can be more than one answer!! I really need help with this question because I am confused on what to do.. /.\

Answer 1

To check whether a triangle is a right triangle given the dimensions, we can apply Pythagorean's theorem. To recall, we have


`a^(2) + b^(2) = c^(2)`

where c is the longest side (or more known as the hypotenuse) and a and b as the shorter sides of the right triangle. All right triangles must satisfy this theorem.

Now, to make this clearer, let's check the first choice: {3, 4, 5}. Substituting the values, we have


`3^(2) + 4^(2) = 5^(2)`

`9 + 16 = 25`

`25 = 25`

This clearly shows that {3, 4, 5} satisfies the theorem and thus confirming that it's a right triangle.

We can use the same reasoning for the rest as shown below.

2) {5, 12, 14}


`5^(2) + 12^(2) \\eq14^(2)`

`25 + 144\\eq156`

`169\\eq156`

3) {4, √24, 8}


`4^(2) + (√(24))^(2)\\eq8^(2)`

`16 + 24\\eq64`

`40\\eq64`

4) {5, 7, √74}


`5^(2) + 7^(2) = (√(74))^(2)`

`25 + 49 = 74`

`74 = 74`

As shown, only 1) and 4) satisfies the theorem. Showing that the two triangles are right triangles.

Answer: 1 and 4