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# Sides of triangles are given below. Determine which of them are right triangles. In case of a right triangle, write the length of its hypotenuse.

3 cm, 8 cm, 6 cm

Given:

The sides of a triangle are $3\ cm, 8\ cm$ and $6\ cm$.

To do:

We have to determine whether the triangle is a right-angled triangle and write the length of its hypotenuse.

Solution:

Let $a=3\ cm$, $b=8\ cm$ and $c=6\ cm$.

We know that,

If the square of the hypotenuse is equal to the sum of the squares of the other two sides, then the triangle is a right-angled triangle.

Therefore,

$(a)^2=(3\ cm)^2=9\ cm^2$

$(b)^2=(8\ cm)^2=64\ cm^2$

$(c)^2=(6\ cm)^2=36\ cm^2$

Here, $(a)^2+(c)^2=(9+36)\ cm^2=45\ cm^2$

$(a)^2+(c)^2≠(b)^2$

The square of larger side is not equal to the sum of squares of other two sides.

Therefore, the given triangle is not right angled.

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