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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.
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
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