Question

Is the triangle a right triangle?
4 6 7
Is this a right triangle?

Answer 1

No, this triangle is not a right triangle.

Explanation:

Step 1: Definition(s)/explanations

• This is a right triangle, so the Pythagorean Theorem applies.
• The Pythagorean Theorem states that the legs of the triangle, squared, must equal the hypotenuse, squared.

• The legs of the triangle are the sides that make the right angle.
• The hypotenuse is the longest side.

Formula:

`pt-a^2+b^2=c^2`

`legs=a,b`

`hypotenuse=c`

Step 2: Solve.

Now, I just plug the numbers into the formula.

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

`4^2+6^2=7^2`

`16+36\\eq 49`

If the legs of the triangle do not equal the hypotenuse, then the triangle cannot be a right triangle.

Step 3: Conclude.

Therefore, the triangle cannot be a right triangle.

Answer 2

No

Explanation:

Given :-

• A triangle with some side measure .
• The sides are 4 ,6,7.

And we need to tell whether it is a right angled triangle or not . It will be a right angled triangle if it follows the Pythagoras Theorem.

Pythagoras Theorem :-

• In right angle triangle the sum of squares of the two smallest sides is equal to the square of the largest side .

Here the two smallest sides are 4 & 6 .

Sum of Squares of 4 and 6 :-

`:\implies` 4² + 6²

`:\implies` 24 + 36

`:\implies` 60

Square of 7 :-

`:\implies` 7²

`:\implies` 49

And :-

• They aren't equal. So the triangle is not a right angled triangle .

Hence the triangle is not a right angle triangle.