Question

Workers at the Pythagorean Construction Company are building a new house. They need to make sure that proper right triangles are formed to ensure that a safe house is built. What statement should the builders use to ensure that right triangles are formed? If the sum of the two shorter sides equals the longest side, then the triangle is a right triangle. If the sum of the squares of the two longer sides equals the square of the shortest side, then the triangle is a right triangle. If the sum of the squares of the two shorter sides equals the square of the longest side, then the triangle is a right triangle. If the difference of the squares of the two shorter sides equals the square of the longest side, then the triangle is a right triangle.

Answer 1

Question:

Workers at the Pythagorean Construction Company are building a new house. They need to make sure that proper right triangles are formed to ensure that a safe house is built. What statement should the builders use to ensure that right triangles are formed.

1. If the sum of the two shorter sides equals the longest side, then the triangle is a right triangle.
2. If the sum of the squares of the two longer sides equals the square of the shortest side, then the triangle is a right triangle.
3. If the sum of the squares of the two shorter sides equals the square of the longest side, then the triangle is a right triangle
4. If the difference of the squares of the two shorter sides equals the square of the longest side, then the triangle is a right triangle.

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Understanding question:

First of all we should understand that what question is saying and what we have to do.

Question is about that some workers of a company are wanting to build as house in the form of right angled triangle. To make safe house, they need to make exactly right angled triangle shape room.

Now, we have given some statement and we have to say that which of the given statement is correct for the given question.

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Answer:

We know that to ensure that given traingle is in the form of right angled triangle or not, we use Pythagoras theorem. Pythagoras theorem State that if square of two shorter side of traingle (height and base) is equal to square of longer side(hypotenuse) of triangle then the given traingle will be right angled triangle.

Now, come on the statements,

First statement is saying that right angled traingle is that triangle in which 'sum of the two shorter sides equals the longest side'. So it not matching with Pythagoras theorem and that's why this statement is wrong

Second statment is saying that right angled triangle is that triangle in 'which sum of the squares of the two longer sides equals the square of the shortest side'. It is also opposite of Pythagoras theorem. So this statement is also wrong.

Third statement is saying that right angled triangle is that triangle in which 'sum of the squares of the two shorter sides equals the square of the longest side'. Is it matching with Pythagoras theorem? Yes, it is matching. So this statement is correct.

Fourth statement is saying that right angled triangle is that triangle in which 'difference of the squares of the two shorter sides equals the square of the longest side'. So it is also not satisfying statement. So it also wrong.

Conclusion:

• Statement 3rd is correct for making right angle triangle shaped house.

Answer 2

Answer:

the answers c

"If the sum of the squares of the two shorter sides equals the square of the longest side, then the triangle is a right triangle."

Step-by-step explanation: