A triangle has side lengths of 3cm, 4cm, and, 6cm. Is it a right triangle explain?
Answer: No, a triangle having side lengths 3cm, 4cm, and, 6cm is not a right triangle.
Let's solve this question step by step.
Let's assume that the given triangle is a right-angled triangle
Here, we are given that
Hypotenuse(h) = 6cm (hypotenuse is the longest side)
Base(b) = 3cm
Altitude(a) = 4cm
According to the Pythagoras theorem, for a given right triangle,
Hypotenuse2 = Altitude2 + Base2
Thus as per the given dimensions,
h2 = a2 + b2
⇒ h2 = 3² + 4² = 9 +16 = 25
According to given hypotenuse h,
h2 = 62 = 36
Since they do not match, we cannot have a right triangle with these measures.
We can use the right angle triangle calculator to check whether the given sides of a triangle belong to the right-angled triangle or not.
Hence, it is not a right-angled triangle as the given dimensions (3cm, 4cm, and, 6cm) of the triangle do not satisfy the Pythagoras theorem.