The sides of certain triangles are given below. Determine which of them are right triangles.
(i) $a\ =\ 7\ cm,\ b\ =\ 24\ cm$ and $c\ =\ 25\ cm$

Given:

The sides of a triangle are $a=7\ cm, b=24\ cm$, and $c=25\ cm$.

To do:

We have to determine whether the triangle is a right-angled triangle.

Solution:

$a=7\ cm$

$b=24\ cm$

$c=25\ cm$

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,

$(a)^2=(7\ cm)^2=49\ cm^2$

$(b)^2=(24\ cm)^2=576\ cm^2$

$(c)^2=(25\ cm)^2=625\ cm^2$

Here, $(a)^2+(b)^2=(49+576)\ cm^2=625\ cm^2$

$(a)^2+(b)^2=(c)^2$

Therefore, by the converse of Pythagoras theorem, the given sides are the sides of a right triangle.

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Updated on: 10-Oct-2022

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