# Which of the following can be the sides of a right triangle?$(i).\ 2.5 cm,\ 6.5 cm,\ 6 cm.$$(ii).\ 2 cm,\ 2 cm,\ 5 cm.$$(iii).\ 1.5 cm,\ 2cm,\ 2.5 cm.$In the case of right-angled triangles, identify the right angles.

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Given:
$(i).\ 2.5 cm,\ 6.5 cm,\ 6 cm.$

$(ii).\ 2 cm,\ 2 cm,\ 5 cm.$

$(iii).\ 1.5 cm,\ 2cm,\ 2.5 cm.$

To do: To write which of the above-given sides can be the sides of a right-angled triangle. In the case of right-angled triangles, the right angle has to be identified.

Solution:

Let the larger side be the hypotenuse and also using Pythagoras theorem,

$(i)$. In triangle $ABC$

$L.H.S.=(AC)^2$

$=(6.5)^2$

$=42.25\ cm^2$

$R.H.S.=(AB)^2+(BC)^2$

$=(6)^2+(2.5)^2$

$=36+6.25$

$=42.25$

On comparing, $LHS=RHS$

Therefore, the given sides are of the right-angled triangle.

$(ii)$. In triangle $ABC$,

$L.H.S.=(AC)^2=5^2$

$=25\ cm^2$

$R.H.S.=(AB)^2+(BC)^2$

$=(2)^2+(2)^2$

$=4+4$

$=8$

On comparing, $LHS≠RHS$

Therefore, the given sides are not of the right-angled triangle.

$(iii)$ In triangle $ABC$,

$L.H.S.=(AC)^2$

$=2.5^2$

$=6.25\ cm^2$

$R.H.S.=(AB)^2+(BC)^2$

$=(2)^2+(1.5)^2$

$=4 +2.25$

$=6.25$

Here, $L.H.S=R.H.S$

Therefore, the given sides are of the right-angled triangle.
Updated on 10-Oct-2022 13:34:30