# 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.50 cm, 80 cm, 100 cm

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Given:

The sides of a triangle are $50\ cm, 80\ cm$ and $100\ cm$.

To do:

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

Solution:

Let $a=50\ cm$, $b=80\ cm$ and $c=100\ cm$.

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,

$(a)^2=(50\ cm)^2=2500\ cm^2$

$(b)^2=(80\ cm)^2=6400\ cm^2$

$(c)^2=(100\ cm)^2=10000\ cm^2$

Here, $(a)^2+(b)^2=(2500+6400)\ cm^2=8900\ cm^2$

$(a)^2+(b)^2≠(c)^2$

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.

Updated on 10-Oct-2022 13:21:24