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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.
50 cm, 80 cm, 100 cm
The sides of a triangle are $50\ cm, 80\ cm$ and $100\ cm$.
We have to determine whether the triangle is a right-angled triangle and write the length of its hypotenuse.
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.
$(a)^2=(50\ cm)^2=2500\ cm^2$
$(b)^2=(80\ cm)^2=6400\ cm^2$
$(c)^2=(100\ cm)^2=10000\ cm^2$
Here, $(a)^2+(b)^2=(2500+6400)\ cm^2=8900\ cm^2$
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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