Question

The lengths of the sides of a triangle are 4,5,6 can the triangle still be a right triangle

Answer 1

No. We can use the pythagorean theorem to prove this.The equation being a2 + b2 = c2. We then use two of  the least of the three numbers, which are 4 and 5, to substitute for “a” and “b”. We get a value for “c” which is 6.4, rounded off to the nearest tenth. This value is greater than 6. Note that this is a very logical way of solving the problem since a greater number for “a” and “b” would lead a greater value for “c”

Answer 2

Hello there! Thank you for asking your question here at Brainly! I will be assisting you with answering this problem, and will teach you how to handle it on your own in the future.

First, we need to understand how the sides of a right triangle work.
There is a rule that geometry users practice to test if there is a proper right triangle. This rule is called the "3,4,5" rule.
This rule is known as the Pythagorean Theorum. The Pythagorean Theorum basically states that one leg of the triangle squared plus the other leg of the triangle squared is equal to the hypotenuse squared.

In written form:
a^2 + b^2 = c^2

To prove that the 3,4,5 rule works, let me apply this to the side lengths.
3 will represent a, 4 will represent b, and 5 will represent c.

3^2 + 4^2 = 5^2
Simplify all three squares.
9 + 16 = 25
25 = 25
This proves the 3,4,5 rule works.

Now, let's try to apply this rule with the side lengths 4, 5, and 6.
4 will represent A, 5 will represent B, and 6 will represent C.

4^2 + 5^2 = 6^2
Simplify the squares.
16 + 25 = 36
41 = 36

This does not apply to the Pythagorean Theorum, thus it is NOT a right triangle.

I hope this helps!