Question

Does a triangle with sides of lengths 1.5 ft, 2.5 ft, and 2 ft form a right triangle? How do you know?

Answer 1

Answer:

Yes, the side lengths of 1.5, 2.5, and 2 ft form a right triangle.

Explanation:

Before we solve this problem, we need to know a couple of things.

In a right triangle, you have two legs and a diagonal line that goes from one leg to the other or from one side to the other. This line is called the hypotenuse. It is the longest side of a right triangle. This length can be calculated by using a special formula that is over a thousand years old.

The formula is called the Pythagorean Theorem.

The formula states that if you square one leg and the other leg and add it up. You get the side of hypotenuse which is squared as well.

Here it is in simple terms: $a^{2} +b^{2} =c^{2}$.

a and b are your two legs.

C is your hypotenuse.

In this case 1.5 and 2 are your legs and 2.5 is your hypotenuse since it is the longest side.

Before we calculate, there is a converse to the Pythagorean Theorem.

If $a^{2} +b^{2} \neq c^{2}$, then it is not a right triangle.

Lets make 1.5 for a

and 2 for b.

We know 2.5 is for c.

Here it is.

$1.5^{2} +2^{2} =2.5^{2}$. The / means it is a fraction.

1.5 squared is 9/4 and 2 squared is 4. Add 4 and 9/4 and you get 25/4 squared. Take the square root of 25/4 and you get 5/2.

5/2 is equal to 2.5, so the Pythagorean Theorem applies to this triangle. Therefore, these side lengths do form a right triangle.

Hope this helps!